# Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems

## Abstract

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.

- Authors:

- Instituto de Fisica Gleb Wataghin, UNICAMP, P.O. Box 6165, 13083-970, Campinas, SP (Brazil)
- (Brazil)

- Publication Date:

- OSTI Identifier:
- 21020193

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.065014; (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; ACTION INTEGRAL; ALGEBRA; LORENTZ TRANSFORMATIONS; NONLINEAR PROBLEMS; PARTICLE MODELS; QUANTUM FIELD THEORY; RELATIVISTIC RANGE; RELATIVITY THEORY; SPACE; SPACE-TIME; SYMMETRY

### Citation Formats

```
Bernardini, A. E., Rocha, R. da, Instituto de Fisica Teorica, UNESP, Rua Pamplona 145, 01405-900, Sao Paulo, SP, and Instituto de Fisica Gleb Wataghin, UNICAMP, P.O. Box 6165, 13083-970, Campinas, SP.
```*Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.065014.

```
Bernardini, A. E., Rocha, R. da, Instituto de Fisica Teorica, UNESP, Rua Pamplona 145, 01405-900, Sao Paulo, SP, & Instituto de Fisica Gleb Wataghin, UNICAMP, P.O. Box 6165, 13083-970, Campinas, SP.
```*Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems*. United States. doi:10.1103/PHYSREVD.75.065014.

```
Bernardini, A. E., Rocha, R. da, Instituto de Fisica Teorica, UNESP, Rua Pamplona 145, 01405-900, Sao Paulo, SP, and Instituto de Fisica Gleb Wataghin, UNICAMP, P.O. Box 6165, 13083-970, Campinas, SP. Thu .
"Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems". United States.
doi:10.1103/PHYSREVD.75.065014.
```

```
@article{osti_21020193,
```

title = {Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems},

author = {Bernardini, A. E. and Rocha, R. da and Instituto de Fisica Teorica, UNESP, Rua Pamplona 145, 01405-900, Sao Paulo, SP and Instituto de Fisica Gleb Wataghin, UNICAMP, P.O. Box 6165, 13083-970, Campinas, SP},

abstractNote = {We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.},

doi = {10.1103/PHYSREVD.75.065014},

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

number = 6,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}