# Planck-scale modified dispersion relations and Finsler geometry

## Abstract

A common feature of all quantum gravity (QG) phenomenology approaches is to consider a modification of the mass-shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such approaches is therefore usually set up in the cotangent bundle (phase space). However it was recently proposed that this phenomenology could be associated with an energy dependent geometry that has been coined 'rainbow metric'. We show here that the latter actually corresponds to a Finsler geometry, the natural generalization of Riemannian geometry. We provide in this way a new and rigorous framework to study the geometrical structure possibly arising in the semiclassical regime of QG. We further investigate the symmetries in this new context and discuss their role in alternative scenarios like Lorentz violation in emergent spacetimes or deformed special relativity-like models.

- Authors:

- SISSA, Via Beirut 2-4, 34014 Trieste (Italy) and INFN, Sezione di Trieste (Italy)

- Publication Date:

- OSTI Identifier:
- 21020161

- 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.75.064015; (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; COSMOLOGY; DISPERSION RELATIONS; ENERGY DEPENDENCE; GEOMETRY; LORENTZ INVARIANCE; PHASE SPACE; QUANTUM GRAVITY; RELATIVISTIC RANGE; RELATIVITY THEORY; RIEMANN SPACE; SEMICLASSICAL APPROXIMATION; SPACE-TIME; SYMMETRY

### Citation Formats

```
Girelli, F., Liberati, S., and Sindoni, L..
```*Planck-scale modified dispersion relations and Finsler geometry*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.064015.

```
Girelli, F., Liberati, S., & Sindoni, L..
```*Planck-scale modified dispersion relations and Finsler geometry*. United States. doi:10.1103/PHYSREVD.75.064015.

```
Girelli, F., Liberati, S., and Sindoni, L.. Thu .
"Planck-scale modified dispersion relations and Finsler geometry". United States.
doi:10.1103/PHYSREVD.75.064015.
```

```
@article{osti_21020161,
```

title = {Planck-scale modified dispersion relations and Finsler geometry},

author = {Girelli, F. and Liberati, S. and Sindoni, L.},

abstractNote = {A common feature of all quantum gravity (QG) phenomenology approaches is to consider a modification of the mass-shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such approaches is therefore usually set up in the cotangent bundle (phase space). However it was recently proposed that this phenomenology could be associated with an energy dependent geometry that has been coined 'rainbow metric'. We show here that the latter actually corresponds to a Finsler geometry, the natural generalization of Riemannian geometry. We provide in this way a new and rigorous framework to study the geometrical structure possibly arising in the semiclassical regime of QG. We further investigate the symmetries in this new context and discuss their role in alternative scenarios like Lorentz violation in emergent spacetimes or deformed special relativity-like models.},

doi = {10.1103/PHYSREVD.75.064015},

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}

}