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Quantum Field Theory on Noncommutative Spaces
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A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
Forward citations
Cited by 13 Pith papers
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A new perspective on non-commutative deformations of field and gauge theories
Star products built from active symmetry transformations give gauge-invariant non-commutative theories under a weakened unimodularity condition, with a planar equivalence theorem keeping internal Feynman structure undeformed.
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UV/IR mixing as an artifact of non-covariant quantisation
UV/IR mixing in noncommutative scalar field theories is shown to be an artifact of a non-covariant quantization choice rather than an intrinsic feature of noncommutativity.
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Indefinite probabilities in quantum spacetime: A deepening of unpredictability
Using the SU_q(2) quantum group for spin rotations yields non-commuting probability operators, implying indefinite probabilities and preventing sharp determination of relative observer orientations.
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Universal $T$-matrices for quantum Poincar\'e groups: contractions and quantum reference frames
A new quantum deformation of the centrally extended Poincaré algebra is introduced whose universal T-matrix contracts to the Galilei T-matrix for quantum reference frames and appears as a central extension of the spac...
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IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
In noncommutative Yukawa theory, the CPT-required pair of interaction orderings converts the one-loop ultraviolet quadratic divergence into an infrared pole that is reachable in the s-channel.
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Numerical Study of Scalar Field Theory on the Fuzzy Onion
The fuzzy onion scalar field theory shows three fuzzy-sphere-like phases with aligned layers, dynamical phase transitions that blur boundaries, and two fitted phase-boundary curves of the form |b| = k1 + k2 sqrt(c).
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On a non-geometric approach to noncommutative gauge theories
A non-geometric bootstrap on the Moyal plane produces noncommutative gauge theories and derives the U(N) fundamental restriction from the requirement that the conserved non-local current be Lie algebra valued.
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Minimal covariant quantum space-time
The minimal covariant quantum space-time M^{1,3}_0 is shown to be a quantized twistor space, an S2 bundle over a k=-1 FLRW space-time, with localized quasi-coherent states.
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Doubly Quantum Mechanics
Replacing SU(2) with SU_q(2) turns measurement probabilities into operators and makes reference-frame alignment between two observers fundamentally imprecise even in the limit of infinitely many exchanged spins.
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Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
Coreductivity and cosymmetry of a Lie bialgebra are defined and shown to characterize when the complementary dual homogeneous space is reductive or symmetric, with applications to κ-deformed Lorentzian spacetimes.
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Canonical quantization of the Pais-Uhlenbeck oscillator with a higher-derivative perturbation: a covariant phase space approach
A covariant phase-space perturbation scheme for the Pais-Uhlenbeck oscillator reproduces the exact low-energy spectrum and commutator while decoupling the Ostrogradsky ghost.
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Weyl Mutations in Quiver Yangians
Weyl group reflections act as Seiberg-like dualities on A_n quiver gauge theories, mapping stability chambers to each other while conjecturally leaving the quiver Yangian Y(sl_{n+1}) invariant.
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Gauge Invariant and Generic Formulation of Magnetic Translations and so(3,1) Curtright-Zachos Generators
Gauge-invariant magnetic translation operators, built from a gauge-covariant pseudo-momentum P, reproduce Curtright-Zachos generators through a rotation-dilatation duality.
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