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- W4323641535 abstract "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." @default.
- W4323641535 created "2023-03-09" @default.
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- W4323641535 date "2023-03-05" @default.
- W4323641535 modified "2023-09-26" @default.
- W4323641535 title "Symmetries of $kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?" @default.
- W4323641535 doi "https://doi.org/10.48550/arxiv.2303.02728" @default.
- W4323641535 hasPublicationYear "2023" @default.
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