Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 052, 22 pages      arXiv:1003.4356
Contribution to the Special Issue “Noncommutative Spaces and Fields”

Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology

Aiyalam P. Balachandran a, Alberto Ibort b, Giuseppe Marmo c and Mario Martone a, c
a) Department of Physics, Syracuse University, Syracuse, NY 13244-1130, USA
b) Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain
c) Dipartimento di Scienze Fisiche, University of Napoli and INFN, Via Cinthia I-80126 Napoli, Italy

Received March 24, 2010, in final form June 08, 2010; Published online June 21, 2010

In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincaré invariance. We present the latest development in the field, in particular the notion of equivalence of such quantum field theories on a noncommutative spacetime, in this regard we work out explicitly the inequivalence between twisted quantum field theories on Moyal and Wick-Voros planes; the duality between deformations of the multiplication map on the algebra of functions on spacetime F(R4) and coproduct deformations of the Poincaré-Hopf algebra HP acting on F(R4); the appearance of a nonassociative product on F(R4) when gauge fields are also included in the picture. The last part of the manuscript is dedicated to the phenomenology of noncommutative quantum field theories in the particular approach adopted in this review. CPT violating processes, modification of two-point temperature correlation function in CMB spectrum analysis and Pauli-forbidden transition in Be4 are all effects which show up in such a noncommutative setting. We review how they appear and in particular the constraint we can infer from comparison between theoretical computations and experimental bounds on such effects. The best bound we can get, coming from Borexino experiment, is >1024 TeV for the energy scale of noncommutativity, which corresponds to a length scale <10−43 m. This bound comes from a different model of spacetime deformation more adapted to applications in atomic physics. It is thus model dependent even though similar bounds are expected for the Moyal spacetime as well as argued elsewhere.

Key words: noncommutative spacetime; quantum field theory; twisted field construction; Poincaré-Hopf algebra.

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