From noncommutative kappa-Minkowski to Minkowski space-time

Jerzy Kowalski-Glikman; Laurent Freidel; Sebastian Nowak

REVIEW

From noncommutative kappa-Minkowski to Minkowski space-time

Laurent Freidel, Jerzy Kowalski-Glikman, Sebastian Nowak

High Energy Physics - Theory · Submitted 15 Dec 2006 · 21 references

Pith's verdict: The algebra is clean and self-contained, but the physics claim rides on a Weyl map whose justification lives in an unpublished companion paper.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 13, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 4 major objections · 7 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-th/0612170 (version 1)

Pith IDEEM7Z6OS, Pith's permanent record of this paper and its review

CitationJerzy Kowalski-Glikman, Laurent Freidel, Sebastian Nowak. "From noncommutative kappa-Minkowski to Minkowski space-time." arXiv:hep-th/0612170 (2006). https://pith.science/paper/EEM7Z6OS

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Worth your time if you work on kappa-Poincaré or DSR phenomenology, with one caveat up front: the headline equivalence is conditional on a map choice the paper does not defend here. The reader's take is basically right, and the stress-test note lands too — the map is where the physics is decided, not the algebra downstream of it. What is actually new and solid: the 4d Weyl map (5) combined with the bicovariant star product (12) gives the Minkowski action (26) with a sqrt(1+box) factor, and the derivation is written out. The integration identity (13) is proved in Eqs. (19)-(24) and I followed it; the algebra checks. The EMT formula (32) for actions of the form phi f(box) phi is a small but genuinely useful lemma, and it reduces correctly to the standard case. The physics punchline — that the free kappa-Minkowski dispersion relation is unmodified, so no energy-dependent speed of light — is a real claim that cuts against [21] and deserves to be on record. Soft spots, in order of weight. First, the map. The paper says 'among all possible choices of Weyl maps one is preferred' and then defers the construction to [15], 'to appear.' That is not a formality: [11],[12] use a different kinetic term, i.e. a different map, and get a different action. So the sqrt(1+box), the tachyon at box = -1, and the unmodified dispersion all hang on a choice justified elsewhere. The equivalence to the actions of [8],[10],[13] is likewise asserted, not shown. Second, the tachyon-removal argument. Divergence of T at M^2 = -1 is a heuristic; the cleaner statement is that the tachyon sits at P_4 = 0, the boundary of the image of (5), where the measure d^4P/P_4 blows up. The authors' own footnote 1 excludes exactly that hyperplane as 'of measure 0' — fine for the Fourier transform, but it is where the tachyon lives, and the paper does not connect the two. Third, the interacting-theory remarks are explicitly speculative and should be read that way. None of this breaks the free-theory derivation. It does mean the paper is a progress report on a larger construction, not a closed result. Who should read it: anyone working on kappa-Minkowski field theory or DSR phenomenology, and anyone who wants the sqrt(1+box) action as a reference point. Send it out; the referee should press on the map and on the tachyon boundary.

Referee report

Major objections (4)

[Paragraph beginning 'First in order to do physics it is convenient to map...', Eq. (5)] The physical claims of the paper — the √(1+□) factor, the tachyon at □=-1, and the unmodified dispersion relation — all depend on the choice of Weyl map P(k) in Eq. (5). The manuscript states that 'among all possible choices of Weyl maps one is preferred' because it preserves the bicovariant calculus and makes the Poincaré action linear, but the construction is deferred to [15], listed as 'to appear'. The paper does cite [20] for the bicovariant differential calculus, which is published, so the choice is not unsupported; nevertheless, a short in-paper argument for why (5) is selected, or at least a sentence stating what changes for the alternative kinetic term used in [11],[12], would make the central claim self-contained. Since the authors already acknowledge the deferral, this is a request for a paragraph, not for a new derivation.
[Paragraph 'It should be stressed that the action (26) is fully equivalent...'] The sentence 'the action (26) is fully equivalent to the κ-Minkowski space action investigated in [8],[?],[10],[13]' asserts an equivalence that is not demonstrated, and the citation list contains an unresolved '[?]'. Please either exhibit the map between the two formulations (even in a footnote) or soften 'fully equivalent' to something like 'equivalent up to the choice of star product'. As written, the reader cannot tell which of the cited actions is meant to match (26) and under what identification of fields.
[Paragraph after Eq. (33), 'In the case of the tachyonic mode...'] The argument that there are no asymptotic tachyonic states rests on the divergence of T at M²=-1, which is a symptom rather than a proof. The precise statement appears to be that the tachyon sits at the boundary P_4=0 of the image of P (in Planck units), which is the hyperplane excluded in footnote 1; but the text says only that 'we initially restricted the momentum space to be such that P²<κ² so that the tachyon is not in the spectra', and that restriction does not by itself exclude □=-1. Please make the boundary argument explicit, and say whether a smeared wavepacket would still show the divergence or whether the divergence is integrable.
[Eq. (33) and the sentence 'note that since m²≪1 the factor in front of expression above is negligible'] The abstract promises a relativistic mode of 'arbitrary mass m', but the prefactor √(1+m²) in Eq. (33) is only negligible for m≪κ. For m of order κ the energy-momentum tensor is rescaled by √(1+m²), which changes the energy density assigned to a Planck-mass particle and is not a small effect. Please state the regime explicitly, or keep the prefactor and discuss its consequences for the 'essentially standard' characterization.

Minor objections (7)

[Paragraph beginning 'We don't expect expect that this latter feature change...'] The sentence contains a doubled word ('expect expect').
[Eq. (29)] The variational derivative is written as '2√−g δS/δgαβ(y)' without the fraction slash, and the metric-variation identities that follow do not distinguish δg^{μν} from δg_{μν}. Please make the notation explicit.
[Footnote 1] The exclusion of the hyperplane P_+=0 is acknowledged as the place where the star product is not well defined. Please say whether the Fourier inversion formulas (16)-(18) are affected at this boundary, since the tachyon discussion in the text appears to place the problematic mode precisely there.
[Eq. (26) and the definition (1-∂4)=√(1+□)] The branch of the square root is not specified. Since the tachyon sits at □=-1, which is the branch point, the choice of branch is not cosmetic and should be stated.
[Paragraph 'We don't expect expect that this latter feature change in the interacting theory...'] The claim that the tachyonic factor will 'appear as a modification of the integration measure over loop momenta but not as a modification of the propagator' is not derived. The quadratic operator in (26) is √(1+□)(□-m²), whose inverse does contain the √(1+□) factor; please clarify whether a field redefinition is intended, and if so, write it down.
[Author affiliation line] The affiliation contains a garbled string ('Wroc/suppress law'); please correct it in production.
[Reference [15]] Reference [15] is listed as 'to appear'; please update it at proof, since several of the paper's load-bearing statements point to it.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Free field theory on kappa-Minkowski space turns out to be an ordinary, if non-local, Minkowski theory with an unmodified dispersion relation.

The reading

The paper asks a concrete question: if you write down a free massive scalar field on $k$-Minkowski space — the noncommutative spacetime where $[x^0,x^i] = -i x^i/κ$ — what does it look like to an ordinary observer who only knows Minkowski space? The authors answer that, with the right choice of star product, it looks like a perfectly Lorentz-invariant local-looking action with infinitely many derivatives: $S = ∫ d^4x [ (1/2)(∂_μφ)^*(1-∂_4)(∂^μφ) + (m^2/2) φ^*(1-∂_4)φ ]$, where $(1-∂_4) = √(1+□)$. The payoff is that the noncommutativity does not survive as a modified dispersion relation for the ordinary particle: the mass-$m$ mode has standard energy-momentum, so in this theory the speed of light is energy-independent, contrary to a body of earlier expectation. What does survive is a second, Planck-mass pole at $□ = -1$, and the authors argue its energy-momentum tensor diverges, so it cannot appear as an asymptotic state. A reader should care because this is a claim that a specific, widely studied candidate quantum spacetime is physically indistinguishable from ordinary field theory at the free level, with the noncommutativity hiding entirely in a measure-like factor.

What carries the argument

The load-bearing object is the integration identity $∫ d^4x φ^†⋆ψ(x) = ∫ d^4x φ^*(x)(1-∂_4)ψ(x)$, with $(1-∂_4) = √(1+□)$, which converts star products into ordinary products at the price of one non-local operator. It is proved by evaluating the star product on plane waves, where $e^{iP(k)·x}⋆e^{iP(p)·x} = e^{iP(kp)·x}$ with the group law $k p = (k_0+p_0, k_i + e^{-k_0}p_i)$, and then showing that the resulting delta function $δ^4(P(k^{-1}p))$ equals $|P_4(p)|δ^4(P(p)-P(k))$ after using the de Sitter constraint $P_4^2 = κ^2 - P^2 + P_0^2$ and the restriction $P_+ = P_0+P_4 > 0$. The same map fixes the invariant measure $dP(k) = e^{3k_0}dk_0d^3k$ and the Jacobian $det(∂P_μ/∂k_ν) = e^{3k_0}P_4(k)$, which is what makes the Fourier transform invertible and the whole construction consistent. In short: the de Sitter geometry of momentum space is what generates the square-root factor, and the square-root factor is what both preserves the standard dispersion relation and isolates the tachyon.

Extended reading notes

Core claim

The central claim is an exact equivalence. Using the Weyl map $P(k)$ that sends $k$-Minkowski plane waves to ordinary plane waves with $P_0 = κ sinh(k_0/κ) + (k^2/2κ)e^{k_0/κ}$ and $P_i = k_i e^{k_0/κ}$ — the map singled out by the bicovariant differential calculus — and the conjugation $(e^{iP(k)·x})^† = e^{iP(k^{-1})·x}$, the authors prove the integration identity $∫ d^4x φ^†⋆ψ = ∫ d^4x φ^*(1-∂_4)ψ$ with $(1-∂_4) = √(1+□)$. Applying it to the $k$-Minkowski action converts the star products into ordinary products and leaves Eq. (26): a manifestly Poincaré-invariant action with a single non-locality, the factor $√(1+□)$. The field equation is $√(1+□)(□-m^2)φ = 0$, so the spectrum contains the ordinary mass-$m$ mode plus a tachyon at $□=-1$, i.e. at the Planck scale. Computing the symmetric energy-momentum tensor for an infinite-derivative theory yields $T_{αβ} = √(1+m^2)(∂_αφ∂_βφ - (1/2)η_{αβ}(∂_μφ∂^μφ + m^2φ^2))$ for the ordinary mode — a standard tensor with an $O(1)$ prefactor — while for the tachyon the same expression carries a $1/√(1+M^2)$ with $M^2=-1$ and diverges. The authors read that divergence as the statement that creating a tachyon costs infinite energy, consistent with the original momentum space having been restricted to $P^2 < κ^2$; hence no asymptotic tachyonic states. They also note the construction is equivalent to the $k$-Minkowski actions studied earlier in the literature, so the physical content is not new, only its Minkowski-space form.

Load-bearing premise

The argument depends on the specific Weyl map and star product of Eqs. (5) and (12) being the physically correct ones, a choice the authors justify by the bicovariant differential calculus but whose full construction and justification they defer to a companion paper listed as to appear; a different but equally Lorentz-covariant map would change the square-root factor, the tachyon, and the dispersion relation.

Editorial extensions

If this is right

For the ordinary mode, the free dispersion relation is exactly the classical one, so any energy-dependent speed of light in this model would have to come from interactions, not from the noncommutative kinematics.
The noncommutativity of $k$-Minkowski space is absorbed into a single operator $√(1+□)$ acting as a modified integration measure, not as a modified propagator — which is what the authors expect to persist in the interacting theory.
The Planck-mass tachyon at $□=-1$ carries a divergent energy-momentum tensor, so it is excluded from the asymptotic Hilbert space and cannot be produced as a free on-shell state.
Because the action is manifestly Poincaré invariant after the map, the Lorentz symmetry of the ordinary Minkowski description is exact rather than deformed at the free level.
Interactions can be built by taking star-product powers $φ⋆φ⋆φ⋆φ$ of a real field, since $(φ⋆φ)^† = φ^†⋆φ^†$; the same square-root factor should then appear in front of the interacting equations of motion.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the square-root factor really acts as a measure rather than a propagator, then loop integrals in the interacting theory would be finite by a power-counting-suppression mechanism rather than by Pauli-Villars-style subtraction; checking this against a one-loop self-energy would be the natural next test.
The claim that the tachyon is unreachable rests on a divergence in $T_{αβ}$ at a single point of the spectrum; a sharper statement would come from showing the tachyon pole lies outside the image of the Weyl map altogether, which the restriction $P^2 < κ^2$ hints at but does not fully establish.
The disagreement with the earlier claim of an energy-dependent speed of light is attributed to a different choice of differential calculus; making that comparison explicit — same field, two calculi, two dispersion relations — would turn a disagreement about frameworks into a computable discriminator.
Because the equivalence is derived for a free field only, the interesting question is whether the map survives gauge fields, where the bicovariant calculus constrains the possible kinetic terms much more tightly.

Original abstract

We show that free $\kappa$-Minkowski space field theory is equivalent to a relativistically invariant, non local, free field theory on Minkowski space-time. The field theory we obtain has in spectrum a relativistic mode of arbitrary mass $m$ and a Planck mass tachyon. We show that while the energy momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory. It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,653 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.73 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.21 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We show that free $\kappa$-Minkowski space field theory is equivalent to a relativistically invariant, non local, free field theory on Minkowski space-time. The field theory we obtain has in spectrum a relativistic mode of arbitrary mass $m$ and a Planck mass tachyon. We show that while the energy momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory. It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that free $\kappa$-Minkowski space field theory is equivalent to a relativistically invariant, non local, free field theory on Minkowski space-time.	result 0.87	0.95	0.89	asserted 1.00
s1	The field theory we obtain has in spectrum a relativistic mode of arbitrary mass $m$ and a Planck mass tachyon.	result 1.00	0.89	0.10	asserted 1.00
s2	We show that while the energy momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory.	result 0.99	0.93	0.10	asserted 1.00
s3	It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent.	result 0.61	0.90	0.15	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (21)

[21]

A. Agostini, G. Amelino-Camelia, M. Arzano, A. Marcian o and R. A. Tacchi, “Generalizing the Noether theorem for Hopf-algebra spacetime symmetries,” arXiv:hep-th/06072 21

View on Pith
[15]

L. Freidel, J. Kowalski-Glikman and S. Nowak, “Star pro duct for κ–Minkowski space-time and ﬁeld theory” to appear

View on Pith
[11]

G. Amelino-Camelia and M. Arzano, “Coproduct and star p roduct in ﬁeld theories on Lie-algebra non-commutative spa ce- times,” Phys. Rev. D 65 (2002) 084044 [arXiv:hep-th/0105120]

View on Pith Pith review arXiv 2002
[12]

M. Dimitrijevic, L. Jonke, L. Moller, E. Tsouchnika, J. Wess and M. Wohlgenannt, “Field theory on kappa-spacetime, ” arXiv:hep-th/0407187; M. Dimitrijevic, F. Meyer, L. Molle r and J. Wess, “Gauge theories on the kappa-Minkowski space- time,” Eur. Phys. J. C 36 (2004) 117 [arXiv:hep-th/0310116]; M. Dimitrijevic, L. Jo nke, L. Moller, E. Tsouchnika, J. Wes...

View on Pith Pith review arXiv 2004
[8]

P. Kosinski, J. Lukierski and P. Maslanka, “Local D = 4 ﬁel d theory on kappa-deformed Minkowski space,” Phys. Rev. D 62 (2000) 025004 [arXiv:hep-th/9902037]

View on Pith Pith review arXiv 2000
[10]

P. Kosinski, P. Maslanka, J. Lukierski and A. Sitarz, “G eneralized kappa-deformations and deformed relativistic scalar ﬁelds on noncommutative Minkowski space,” arXiv:hep-th/0 307038

View on Pith
[13]

M. Daszkiewicz, K. Imilkowska, J. Kowalski-Glikman an d S. Nowak, “Scalar ﬁeld theory on kappa-Minkowski space-ti me and doubly special relativity,” Int. J. Mod. Phys. A 20, 4925 (2005) [arXiv:hep-th/0410058]

View on Pith Pith review arXiv 2005
[20]

A. Sitarz, “Noncommutative diﬀerential calculus on th e kappa Minkowski space,” Phys. Lett. B 349 (1995) 42 [arXiv:hep-th/9409014]

View on Pith Pith review arXiv 1995
[1]

S. Majid and H. Ruegg, “Bicrossproduct structure of kapp a Poincare group and noncommutative geometry,” Phys. Lett. B 334 (1994) 348 [arXiv:hep-th/9405107]

View on Pith Pith review arXiv 1994
[2]

J. Lukierski, H. Ruegg and W. J. Zakrzewski, “Classical q uantum mechanics of free kappa relativistic systems,” Anna ls Phys. 243 (1995) 90 [arXiv:hep-th/9312153]

View on Pith Pith review arXiv 1995
[3]

J. Lukierski, H. Ruegg, A. Nowicki and V. N. Tolstoi, “Q de formation of Poincar´ e algebra,” Phys. Lett. B 264 (1991) 331; J. Lukierski, A. Nowicki and H. Ruegg, “New quantum Poincare algebra and k deformed ﬁeld theory,” Phys. Lett. B 293 (1992) 344

View on Pith 1991
[4]

G. Amelino-Camelia, “Testable scenario for relativity with minimum-length,” Phys. Lett. B 510, 255 (2001) [arXiv:hep-th/0012238]

View on Pith Pith review arXiv 2001
[5]

G. Amelino-Camelia, “Relativity in space-times with sh ort-distance structure governed by an observer-independe nt (Planckian) length scale,” Int. J. Mod. Phys. D 11, 35 (2002) [arXiv:gr-qc/0012051]

View on Pith Pith review arXiv 2002
[6]

N. R. Bruno, G. Amelino-Camelia and J. Kowalski-Glikman , “Deformed boost transformations that saturate at the Plan ck scale,” Phys. Lett. B 522 (2001) 133 [arXiv:hep-th/0107039]

View on Pith Pith review arXiv 2001
[7]

J. Kowalski-Glikman, “Introduction to doubly special r elativity,” Lect. Notes Phys. 669 (2005) 131 [arXiv:hep-th/0405273]

View on Pith Pith review arXiv 2005
[9]

P. Kosinski, P. Maslanka, J. Lukierski and A. Sitarz, “To wards kappa-deformed D = 4 relativistic ﬁeld theory,” Czech . J. Phys. 48 (1998) 1407

View on Pith 1998
[14]

N. Moeller and B. Zwiebach, “Dynamics with inﬁnitely ma ny time derivatives and rolling tachyons,” JHEP 0210, 034 (2002) [arXiv:hep-th/0207107]

View on Pith Pith review arXiv 2002
[16]

J. Kowalski-Glikman and S. Nowak, “Doubly special rela tivity and de Sitter space,” Class. Quant. Grav. 20 (2003) 4799 [arXiv:hep-th/0304101]

View on Pith Pith review arXiv 2003
[17]

G. Amelino-Camelia and S. Majid, “Waves on noncommutat ive spacetime and gamma-ray bursts,” Int. J. Mod. Phys. A 15, 4301 (2000) [arXiv:hep-th/9907110]

View on Pith Pith review arXiv 2000
[18]

L. Freidel and S. Majid, “Noncommutative harmonic anal ysis, sampling theory and the Duﬂo map in 2+1 quantum gravity,” arXiv:hep-th/0601004

View on Pith Pith review arXiv
[19]

L. Freidel and E. R. Livine, “Ponzano-Regge model revis ited. III: Feynman diagrams and eﬀective ﬁeld theory,” Clas s. Quant. Grav. 23 (2006) 2021 [arXiv:hep-th/0502106]. L. Freidel and E. R. Li vine, “Eﬀective 3d quantum gravity and non-commutative quantum ﬁeld theory,” Phys. Rev. Lett. 96, 221301 (2006) [arXiv:hep-th/0512113]

View on Pith Pith review arXiv 2006

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Scalar Field Theory on Non-commutative Snyder Space-Time
hep-th 2010-03 conditional novelty 6.0 of 10

A self-interacting scalar field theory is defined on Snyder non-commutative space-time by using coordinate realizations to fix the ordering ambiguity of the non-associative momentum co-product.
Fock space, quantum fields and kappa-Poincar\'e symmetries
hep-th 2007-07 conditional novelty 6.0 of 10

A Fock space for a scalar field with κ-Poincaré symmetries is constructed, featuring a Planckian momentum cutoff and a deformed bosonization of multiparticle states.
Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
hep-th 2007-06 conditional novelty 6.0 of 10

The standard formulation of scalar field theory on kappa-Minkowski space contains a trans-Planckian mode whose conserved particle number is not a Lorentz scalar, so the theory breaks Lorentz invariance.
Covariant realizations of kappa-deformed space
hep-th 2007-02 conditional novelty 6.0 of 10

Infinitely many rotation-covariant realizations of kappa-deformed Euclidean space are constructed, with matching coproducts and star products, and the type I family is shown to be related by similarity transformations.
Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
hep-th 2009-03 conditional novelty 5.0 of 10

A covariant particle-exchange operator for kappa-Minkowski space is built to first order in the deformation parameter using only Poincare generators, and the resulting R-matrix differs from the twisted one.

Show 3 more citing papers

kappa-Minkowski spacetime as the result of Jordanian twist deformation
math-ph 2008-12 conditional novelty 5.0 of 10

Two twist families generate the same kappa-Minkowski noncommutative spacetime but different deformed dispersion relations, with the minimal Jordanian case giving a linear energy-dependent mass shift.
Twisted Statistics in kappa-Minkowski Spacetime
hep-th 2008-02 conditional novelty 5.0 of 10

For a special class of realizations of kappa-Minkowski space, the twisted flip operator that defines particle statistics is independent of the ordering prescription.
Kappa-Minkowski space-time and the star product realizations
hep-th 2007-05 conditional novelty 5.0 of 10

For any realization of kappa-Minkowski space the star product is derived, and the free scalar field theory built on the natural realization is shown to equal a nonlocal, Lorentz-invariant theory on ordinary Minkowski ...

How the literature uses it

33 arXiv papers cite this in 76 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Utilizing the properties of the {\em{natural}} realization, we construct a scalar field theory on $ \kappa$-deformed Minkowski space and show that it is equivalent to the scalar, nonlocal, relativistically invariant field theory on the ordinary Minkowski space.

Kappa-Minkowski space-time and the star product realizations · 0.97

Papers citing it · 45 sentences without a confident label

Uses its method or tool 1 paper

To do that we will make use of the star product formalism, using the techniques worked out in [ref] .

Star product and interacting fields on $\kappa$-Minkowski space · Introduction · 1.00

Compares with it 1 paper

However, while the effective field theory has the braided category structure because of the invariance of the Haar measure $d(g^-1g'g)=dg'$, the measure of the momentum space of the field theory on $κ$-Minkowski spacetime is only left-invariant [ref] .

Braided quantum field theories and their symmetries · Summary and comments · 0.87

Cites it as background 20 papers

Let us start with recalling some facts from [ref] .

Star product and interacting fields on $\kappa$-Minkowski space · Introduction · 0.84
Only recently however a theory of fields living on this space has started being analyzed in depth [ref] , [ref] , [ref] , [ref] .

$\kappa$-Minkowski space, scalar field, and the issue of Lorentz invariance · Introduction · 0.88
The other frequently discussed example, which will be considered in this paper, is the $κ$-Minkowski noncommutativity [ref] , where only the linear term in the expansion [ref] is retained: [equation] In this case $θ_μν^(1)^ρ$ is of the special form [equation] Such a theory is often invoked as a possible candidate for the effective low energy description of quantum gravity [ref] .

Low-energy constraints on kappa-Minkowski extension of the Standard Model · Introduction · 0.88

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [21]

A. Agostini, G. Amelino-Camelia, M. Arzano, A. Marcian o and R. A. Tacchi, “Generalizing the Noether theorem for Hopf-algebra spacetime symmetries,” arXiv:hep-th/06072 21

View on Pith

[2] [15]

L. Freidel, J. Kowalski-Glikman and S. Nowak, “Star pro duct for κ–Minkowski space-time and ﬁeld theory” to appear

View on Pith

[3] [11]

G. Amelino-Camelia and M. Arzano, “Coproduct and star p roduct in ﬁeld theories on Lie-algebra non-commutative spa ce- times,” Phys. Rev. D 65 (2002) 084044 [arXiv:hep-th/0105120]

View on Pith Pith review arXiv 2002

[4] [12]

M. Dimitrijevic, L. Jonke, L. Moller, E. Tsouchnika, J. Wess and M. Wohlgenannt, “Field theory on kappa-spacetime, ” arXiv:hep-th/0407187; M. Dimitrijevic, F. Meyer, L. Molle r and J. Wess, “Gauge theories on the kappa-Minkowski space- time,” Eur. Phys. J. C 36 (2004) 117 [arXiv:hep-th/0310116]; M. Dimitrijevic, L. Jo nke, L. Moller, E. Tsouchnika, J. Wes...

View on Pith Pith review arXiv 2004

[5] [8]

P. Kosinski, J. Lukierski and P. Maslanka, “Local D = 4 ﬁel d theory on kappa-deformed Minkowski space,” Phys. Rev. D 62 (2000) 025004 [arXiv:hep-th/9902037]

View on Pith Pith review arXiv 2000

[6] [10]

P. Kosinski, P. Maslanka, J. Lukierski and A. Sitarz, “G eneralized kappa-deformations and deformed relativistic scalar ﬁelds on noncommutative Minkowski space,” arXiv:hep-th/0 307038

View on Pith

[7] [13]

M. Daszkiewicz, K. Imilkowska, J. Kowalski-Glikman an d S. Nowak, “Scalar ﬁeld theory on kappa-Minkowski space-ti me and doubly special relativity,” Int. J. Mod. Phys. A 20, 4925 (2005) [arXiv:hep-th/0410058]

View on Pith Pith review arXiv 2005

[8] [20]

A. Sitarz, “Noncommutative diﬀerential calculus on th e kappa Minkowski space,” Phys. Lett. B 349 (1995) 42 [arXiv:hep-th/9409014]

View on Pith Pith review arXiv 1995

[9] [1]

S. Majid and H. Ruegg, “Bicrossproduct structure of kapp a Poincare group and noncommutative geometry,” Phys. Lett. B 334 (1994) 348 [arXiv:hep-th/9405107]

View on Pith Pith review arXiv 1994

[10] [2]

J. Lukierski, H. Ruegg and W. J. Zakrzewski, “Classical q uantum mechanics of free kappa relativistic systems,” Anna ls Phys. 243 (1995) 90 [arXiv:hep-th/9312153]

View on Pith Pith review arXiv 1995

[11] [3]

J. Lukierski, H. Ruegg, A. Nowicki and V. N. Tolstoi, “Q de formation of Poincar´ e algebra,” Phys. Lett. B 264 (1991) 331; J. Lukierski, A. Nowicki and H. Ruegg, “New quantum Poincare algebra and k deformed ﬁeld theory,” Phys. Lett. B 293 (1992) 344

View on Pith 1991

[12] [4]

G. Amelino-Camelia, “Testable scenario for relativity with minimum-length,” Phys. Lett. B 510, 255 (2001) [arXiv:hep-th/0012238]

View on Pith Pith review arXiv 2001

[13] [5]

G. Amelino-Camelia, “Relativity in space-times with sh ort-distance structure governed by an observer-independe nt (Planckian) length scale,” Int. J. Mod. Phys. D 11, 35 (2002) [arXiv:gr-qc/0012051]

View on Pith Pith review arXiv 2002

[14] [6]

N. R. Bruno, G. Amelino-Camelia and J. Kowalski-Glikman , “Deformed boost transformations that saturate at the Plan ck scale,” Phys. Lett. B 522 (2001) 133 [arXiv:hep-th/0107039]

View on Pith Pith review arXiv 2001

[15] [7]

J. Kowalski-Glikman, “Introduction to doubly special r elativity,” Lect. Notes Phys. 669 (2005) 131 [arXiv:hep-th/0405273]

View on Pith Pith review arXiv 2005

[16] [9]

P. Kosinski, P. Maslanka, J. Lukierski and A. Sitarz, “To wards kappa-deformed D = 4 relativistic ﬁeld theory,” Czech . J. Phys. 48 (1998) 1407

View on Pith 1998

[17] [14]

N. Moeller and B. Zwiebach, “Dynamics with inﬁnitely ma ny time derivatives and rolling tachyons,” JHEP 0210, 034 (2002) [arXiv:hep-th/0207107]

View on Pith Pith review arXiv 2002

[18] [16]

J. Kowalski-Glikman and S. Nowak, “Doubly special rela tivity and de Sitter space,” Class. Quant. Grav. 20 (2003) 4799 [arXiv:hep-th/0304101]

View on Pith Pith review arXiv 2003

[19] [17]

G. Amelino-Camelia and S. Majid, “Waves on noncommutat ive spacetime and gamma-ray bursts,” Int. J. Mod. Phys. A 15, 4301 (2000) [arXiv:hep-th/9907110]

View on Pith Pith review arXiv 2000

[20] [18]

L. Freidel and S. Majid, “Noncommutative harmonic anal ysis, sampling theory and the Duﬂo map in 2+1 quantum gravity,” arXiv:hep-th/0601004

View on Pith Pith review arXiv

[21] [19]

L. Freidel and E. R. Livine, “Ponzano-Regge model revis ited. III: Feynman diagrams and eﬀective ﬁeld theory,” Clas s. Quant. Grav. 23 (2006) 2021 [arXiv:hep-th/0502106]. L. Freidel and E. R. Li vine, “Eﬀective 3d quantum gravity and non-commutative quantum ﬁeld theory,” Phys. Rev. Lett. 96, 221301 (2006) [arXiv:hep-th/0512113]

View on Pith Pith review arXiv 2006