Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
| Autor: | Nandi, Partha, Chakraborty, Anwesha, Pal, Sayan Kumar, Chakraborty, Biswajit, Scholtz, Frederik G |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | JHEP 07 (2023) 142 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP07(2023)142 |
| Popis: | The quest for a quantum gravity phenomenology has inspired a quantum notion of space-time, which motivates us to study the fate of the relativistic symmetries of a particular model of quantum space-time, as well as its intimate connection with the plausible emergent curved "physical momentum space". We here focus on the problem of Poincare symmetry of $\kappa$-Minkowski type non-commutative (quantum) space-time, where the Poincare algebra, on its own, remains undeformed, but in order to retain the structure of the space-time non-commutative (NC) algebra, action of the algebra generators on the operator-valued space-time manifold must be enveloping algebra valued that lives in entire phase space i.e. the cotangent bundle on the space-time manifold (at classical level). Further, we constructed a model for a spin-less relativistic massive particle enjoying the deformed Poincare symmetry, using the first order form of geometric Lagrangian, that satisfies a new deformed dispersion relation and explored a feasible regime of a future Quantum Gravity theory in which the momentum space becomes curved. In this scenario there is only a mass scale (Planck mass $m_{p}$), but no length scale. Finally, we relate the deformed mass shell to the geodesic distance in this curved momentum space, where the mass of the particle gets renormalized as a result of noncommutativity. We show, that under some circumstances, the Planck mass provides an upper bound for the observed renormalized mass. Comment: 34 pages, One appendix added and section 2.1 extended |
| Databáze: | arXiv |
| Externí odkaz: |
|