Full twisted Poincaré symmetry and quantum field theory on Moyal-Weyl spaces

作者: Gaetano Fiore , Julius Wess

DOI: 10.1103/PHYSREVD.75.105022

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摘要: We explore some general consequences of a proper, full enforcement the 'twisted Poincare' covariance Chaichian et al., Wess, Koch and Oeckl upon many-particle quantum mechanics field quantization on Moyal-Weyl noncommutative space(time). This entails associated braided tensor product with an involutive braiding (or *-tensor in parlance Aschieri al.) prescription for any coordinate pair x, y generating two different copies space(time); nontrivial commutation relations between them imply that x-y is central its Poincare transformation properties remain undeformed. As consequence, theory (QFT) (even space-time noncommutativity) one can reproduce notions (like spacelike separation, time- normal-ordering, Wightman or Green's functions, etc.), impose constraints (Wightman axioms), construct free interacting theories which essentially coincide undeformed ones, since only observable quantities involve differences. In other words, may thus well realize (QM) QFT's where effect space(time) noncommutativity amounts to practically unobservable common translation all reference frames.

参考文章(71)
Thomas Filk, Divergencies in a field theory on quantum space Physics Letters B. ,vol. 376, pp. 53- 58 ,(1996) , 10.1016/0370-2693(96)00024-X
M. Chaichian, M. N. Mnatsakanova, K. Nishijima, A. Tureanu, Yu. S. Vernov, Toward an axiomatic formulation of noncommutative quantum field theory Journal of Mathematical Physics. ,vol. 52, pp. 032303- 032303 ,(2011) , 10.1063/1.3567411
Paolo Aschieri, Christian Blohmann, Marija Dimitrijević, Frank Meyer, Peter Schupp, Julius Wess, A gravity theory on noncommutative spaces Classical and Quantum Gravity. ,vol. 22, pp. 3511- 3532 ,(2005) , 10.1088/0264-9381/22/17/011
Gaetano Fiore, Peter Schupp, Identical Particles and Quantum Symmetries Nuclear Physics. ,vol. 470, pp. 211- 235 ,(1996) , 10.1016/0550-3213(96)00157-5
Marija Dimitrijević, Marija Dimitrijević, Marija Dimitrijević, Julius Wess, Julius Wess, Paolo Aschieri, Frank Meyer, Frank Meyer, Noncommutative geometry and gravity Classical and Quantum Gravity. ,vol. 23, pp. 1883- 1911 ,(2006) , 10.1088/0264-9381/23/6/005
Biswajit Chakraborty, Sunandan Gangopadhyay, Arindam Ghosh Hazra, Frederik G Scholtz, Twisted Galilean symmetry and the Pauli principle at low energies Journal of Physics A. ,vol. 39, pp. 9557- 9572 ,(2006) , 10.1088/0305-4470/39/30/011
Nathan Seiberg, Shiraz Minwalla, Mark Van Raamsdonk, Noncommutative perturbative dynamics Journal of High Energy Physics. ,vol. 2000, pp. 020- 020 ,(2000) , 10.1088/1126-6708/2000/02/020
D. Bahns, S. Doplicher, K. Fredenhagen, G. Piacitelli, Field theory on noncommutative spacetimes: Quasiplanar Wick products Physical Review D. ,vol. 71, pp. 025022- ,(2005) , 10.1103/PHYSREVD.71.025022
Fedele Lizzi, Sachindeo Vaidya, Patrizia Vitale, Twisted conformal symmetry in noncommutative two-dimensional quantum field theory Physical Review D. ,vol. 73, pp. 125020- ,(2006) , 10.1103/PHYSREVD.73.125020
Alexander B Zamolodchikov, Alexey B Zamolodchikov, Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models Annals of Physics. ,vol. 120, pp. 253- 291 ,(1979) , 10.1016/0003-4916(79)90391-9