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Noncommutative Field Theory
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Noncommutative Field Theory
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We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, both on the classical and quantum level. To appear in Reviews of Modern Physics.
Forward citations
Cited by 11 Pith papers
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Indefinite probabilities in quantum spacetime: A deepening of unpredictability
SU_q(2) quantum group applied to spin-1/2 rotations yields non-commuting probability operators, an uncertainty principle for probabilities, and non-commutative rotation matrices between observers.
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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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Indefinite probabilities in quantum spacetime: A deepening of unpredictability
SU_q(2) rotational symmetry turns spin probabilities into non-commuting operators, yielding an uncertainty principle that prevents sharp measurement of relative observer orientations.
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From Noncommutative Kinematics to \(U(1)_{\star}\) Gauge Theory: A Family of Spectral Triples with Localized Gauge-induced Perturbations
Spectral triples are constructed for noncommutative kinematics with G_NC parameters, and localized U(1)_* gauge perturbations are shown to converge strongly in resolvent to the minimally coupled Dirac operator as cuto...
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Batalin-Vilkovisky quantization with an angular twist
Two inequivalent noncommutative QFTs are built on λ-Minkowski space: a braided version with logarithmic UV divergences and no UV/IR mixing, and a standard version with periodic UV/IR mixing where non-planar correlator...
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Poisson Gauge Theories in Three Dimensions: Exact Solutions and Conservation Laws
Exact solutions to noncommutative 3D Maxwell-Chern-Simons theory yield finite energy for point charges, permit arbitrary magnetic flux through non-perturbative dependence on the deformation parameter, and include a ge...
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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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Quantum Spacetime, Quantum Gravity and Gravitized Quantum Theory
Quantum spacetime with a non-commutative dual explains the fixed Born rule of quantum theory and leads to gravitized quantum mechanics featuring dynamical probabilities and higher-order interference.
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Nonlocal four-fermion theory
Hyperbolic Dirac form factors lower the critical coupling for dynamical mass generation in a nonlocal NJL/GN model, while oscillatory form factors raise it.
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Noncommutative black holes: Topological bulk-boundary correspondence and Binary Merger Bounds
For noncommutative RN-AdS black holes, the paper claims bulk and boundary thermodynamic topological charges equal to zero and derives perturbative second-law corrections to the remnant-mass bound.
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Branes
A review of branes in string theory covering their multiple descriptions and interaction phenomena.
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