RECORD
Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism
High Energy Physics - Theory · Submitted 6 Aug 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, $\alpha = a/T$.
The compiled record
The paper's own sentences, arranged. 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.
Open the compiled record
The abstract, sentence by sentence
We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, $\alpha = a/T$. In the Wick-rotated Rindler hyperbolic coordinates, the KMS relations reduce to standard (anti-)periodic boundary conditions in terms of the imaginary proper time (rapidity) coordinate. Our findings pave the way to study, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe and early stages of quark-gluon plasma created in relativistic heavy-ion collisions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. | background 0.58 | 0.53 | 0.04 | asserted 0.65 |
| s1 | We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. | result 0.96 | 0.87 | 0.08 | asserted 1.00 |
| s2 | We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, $\alpha = a/T$. | result 0.95 | 0.93 | 0.69 | asserted 1.00 |
| s3 | In the Wick-rotated Rindler hyperbolic coordinates, the KMS relations reduce to standard (anti-)periodic boundary conditions in terms of the imaginary proper time (rapidity) coordinate. | result 0.97 | 0.90 | 0.15 | asserted 1.00 |
| s4 | Our findings pave the way to study, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe and early stages of quark-gluon plasma created in relativistic heavy-ion collisions. | future work 0.99 | 0.36 | 0.09 | hedged possibility 0.64 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, $\alpha = a/T$. In the Wick-rotated Rindler hyperbolic coordinates, the KMS relations reduce to standard (anti-)periodic boundary conditions in terms of the imaginary proper time (rapidity) coordinate. Our findings pave the way to study, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe and early stages of quark-gluon plasma created in relativistic heavy-ion collisions.
Human review
References
How the literature uses it
4 arXiv papers cite this in 9 sentences
Papers citing it · 5 sentences without a confident label
Cites it as support 1 paper
-
In an accelerating medium, the thermal quadratic fluctuations of the scalar field decrease [ref] : [equation] This relation is re-derived in the Appendix.
Acceleration as refrigeration: Acceleration-induced spontaneous symmetry breaking in thermal medium · Introduction · 0.97
Cites it as background 2 papers
-
The system, however, is not uniform: the local temperature $T$, the local four-velocity $u^μ$, and the local proper acceleration $a^μ≡u^ν∂_νu^μ$ of particles accelerated along the direction $z$ are constrained to be particular functions of coordinates (see, e.g., a brief summary in Ref. [ref] ): [equation] with vanishing transverse components for the four-velocity, $u^x = u^y = 0$, and the four-acceleration, $a^x = a^y = 0$.
Acceleration as refrigeration: Acceleration-induced spontaneous symmetry breaking in thermal medium · Introduction · 0.81
-
Since particles beyond this horizon cannot reach the accelerated observer, the observer perceives the Minkowski vacuum as a thermal bath of particles at the Unruh temperature [ref] [equation] where $α$ is the acceleration[To avoid confusion with lattice spacing $a$, in our paper acceleration is designated as $α$, which differs from the commonplace designation for the thermal acceleration $α$ (see, for instance, Ref. [ref] ).], $ħ$ is the Planck constant, $k$ is the Boltzmann constant, and $c$ is the speed of light.[In what follows it is assumed that $ħ=c=k=1$.] The formula for the Unruh temperature represents an intriguing interplay between gravity, quantum field theory, and statistical physics, which continues to attract the interest of various theoretical groups (see, for instance, [ref] ).
Spatial confinement-deconfinement transition in accelerated gluodynamics within lattice simulation · Introduction · 0.97
What it cites · 40 sentences without a confident label
Uses data or values from 1 paper
-
In the case of non-central collisions, the angular velocity of the quark-gluon fluid can reach values of the order of $Ω∼10^22 Hz$ [ref] which translates to $ħΩ≃6 MeV ≪T_c$, where $T_c$ is the transition temperature to the quark-gluon plasma phase.
Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid · Introduction · 0.89
Compares with 6 papers
-
In the scalar case, we find for the components of eq_Theta_munu: [equation] with $G_n(α) = ∑_j = 1^∞[sin(jα/ 2)]^-n$, in complete agreement with the results in Ref. [ref] .
Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: scalar field · Energy-momentum tensor with the accelerated KMS conditions · 0.99
-
Subtracting the vacuum ($j=0$) term that diverges in the $ΔX →0$ limit, we get for the scalar fluctuations: [equation] which agrees with the known result [ref] .
Thermal loops in the accelerating frame · Energy-momentum tensor with the accelerated KMS conditions · 0.98
-
In the case of the Dirac field, one can easily check that $ℰ_D = 3𝒫_D$ and $π_D^s = 0$, while [equation] with $S_n(α) = -∑_j = 1^∞(-1)^j cos(jα/2) / [sin(jα/ 2)]^n →S_n(β_Tϕ) ≡i^n S_n(i β_T ϕ) = - ∑_j=1^∞(-1)^j cosh(jβ_T ϕ/2) / [sinh(jβ_Tϕ/2)]^n$, which agrees with the results obtained in Ref. [ref] .
Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field · Energy-momentum tensor with the accelerated KMS conditions · 0.99
Cites as support 4 papers
-
This property, for $α= 2 π$, has been observed in Refs. [ref] .
Unruh effect for fermions from the Zubarev density operator · Geometrical meaning of the accelerated KMS relation in imaginary-time formalism · 0.97
-
This property, for $α= 2 π$, has been observed in Refs. [ref] .
Calculation of acceleration effects using the Zubarev density operator · Geometrical meaning of the accelerated KMS relation in imaginary-time formalism · 0.97
-
This property, for $α= 2 π$, has been observed in Refs. [ref] .
Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: scalar field · Geometrical meaning of the accelerated KMS relation in imaginary-time formalism · 0.97
Cites as background 2 papers
-
From a classical point of view, global equilibrium states in generic particle systems are characterized by the inverse temperature four-vector $β^μ≡u^μ(x) / T(x)$, associated with the local fluid velocity $u^μ$, with $β^μ$ satisfying the Killing equation, $∂_μβ_ν+ ∂_νβ_μ= 0$ [ref] .
Covariant statistical mechanics and the stress-energy tensor · Global equilibrium in uniform acceleration · 0.90
-
In the past decades, there has been a renewed interest in studying systems with acceleration as toy models for understanding the dynamics of the quark-gluon plasma fireball created in ultrarelativistic (non-central) heavy-ion collisions [ref] .
Thermal Hadronization and Hawking-Unruh Radiation in QCD · Introduction · 0.85
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.