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

## Abstract

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

- Authors:

- Dip. di Matematica e Applicazioni, Universita 'Federico II', V. Claudio 21, 80125 Naples (Italy)
- (Italy)
- (Germany)
- Arnold Sommerfeld Center for Theoretical Physics, Universitaet Muenchen, Theresienstr. 37, 80333 Munich (Germany)

- Publication Date:

- OSTI Identifier:
- 20933307

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.105022; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMMUTATION RELATIONS; COORDINATES; GREEN FUNCTION; POINCARE GROUPS; QUANTIZATION; QUANTUM FIELD THEORY; QUANTUM MECHANICS; SPACE-TIME; SYMMETRY; TRANSFORMATIONS

### Citation Formats

```
Fiore, Gaetano, INFN, Sez. di Napoli, Complesso MSA, V. Cintia, 80126 Naples, Arnold Sommerfeld Center for Theoretical Physics, Universitaet Muenchen, Theresienstr. 37, 80333 Munich, Wess, Julius, Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Munich, and Universitaet Hamburg, II Institut fuer Theoretische Physik and DESY, Luruper Chaussee 149, 22761 Hamburg.
```*Full twisted Poincare symmetry and quantum field theory on Moyal-Weyl spaces*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.105022.

```
Fiore, Gaetano, INFN, Sez. di Napoli, Complesso MSA, V. Cintia, 80126 Naples, Arnold Sommerfeld Center for Theoretical Physics, Universitaet Muenchen, Theresienstr. 37, 80333 Munich, Wess, Julius, Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Munich, & Universitaet Hamburg, II Institut fuer Theoretische Physik and DESY, Luruper Chaussee 149, 22761 Hamburg.
```*Full twisted Poincare symmetry and quantum field theory on Moyal-Weyl spaces*. United States. doi:10.1103/PHYSREVD.75.105022.

```
Fiore, Gaetano, INFN, Sez. di Napoli, Complesso MSA, V. Cintia, 80126 Naples, Arnold Sommerfeld Center for Theoretical Physics, Universitaet Muenchen, Theresienstr. 37, 80333 Munich, Wess, Julius, Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Munich, and Universitaet Hamburg, II Institut fuer Theoretische Physik and DESY, Luruper Chaussee 149, 22761 Hamburg. Tue .
"Full twisted Poincare symmetry and quantum field theory on Moyal-Weyl spaces". United States.
doi:10.1103/PHYSREVD.75.105022.
```

```
@article{osti_20933307,
```

title = {Full twisted Poincare symmetry and quantum field theory on Moyal-Weyl spaces},

author = {Fiore, Gaetano and INFN, Sez. di Napoli, Complesso MSA, V. Cintia, 80126 Naples and Arnold Sommerfeld Center for Theoretical Physics, Universitaet Muenchen, Theresienstr. 37, 80333 Munich and Wess, Julius and Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Munich and Universitaet Hamburg, II Institut fuer Theoretische Physik and DESY, Luruper Chaussee 149, 22761 Hamburg},

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

doi = {10.1103/PHYSREVD.75.105022},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}