Fate of $κ$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
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| Format: | Preprint |
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2024
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| _version_ | 1866909494783508480 |
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| author | Bose, Deeponjit Chakraborty, Anwesha Chakraborty, Biswajit |
| author_facet | Bose, Deeponjit Chakraborty, Anwesha Chakraborty, Biswajit |
| contents | Here, we present an algebraic and kinematical analysis of non-commutative $κ$-Minkowski spaces within Galilean (non-relativistic) and Carrollian (ultra-relativistic) regimes. Utilizing the theory of Wigner-Inönu contractions, we begin with a brief review of how one can apply these contractions to the well-known Poincaré algebra, yielding the corresponding Galilean (both massive and mass-less) and Carrollian algebras as $c \to \infty$ and $c\to 0$, respectively. Subsequently, we methodically apply these contractions to non-commutative $κ$-deformed spaces, revealing compelling insights into the interplay among the non-commutative parameters $a^μ$ (with $|a^ν|$ being of the order of Planck length scale) and the speed of light $c$ as it approaches both infinity and zero. Our exploration predicts a sort of "branching" of the non-commutative parameters $a^μ$, leading to the emergence of a novel length scale and time scale in either limit. Furthermore, our investigation extends to the examination of curved momentum spaces and their geodesic distances in appropriate subspaces of the $κ$-deformed Newtonian and Carrollian space-times. We finally delve into the study of their deformed dispersion relations, arising from these deformed geodesic distances, providing a comprehensive understanding of the nature of these space-times. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_05769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fate of $κ$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes Bose, Deeponjit Chakraborty, Anwesha Chakraborty, Biswajit High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Here, we present an algebraic and kinematical analysis of non-commutative $κ$-Minkowski spaces within Galilean (non-relativistic) and Carrollian (ultra-relativistic) regimes. Utilizing the theory of Wigner-Inönu contractions, we begin with a brief review of how one can apply these contractions to the well-known Poincaré algebra, yielding the corresponding Galilean (both massive and mass-less) and Carrollian algebras as $c \to \infty$ and $c\to 0$, respectively. Subsequently, we methodically apply these contractions to non-commutative $κ$-deformed spaces, revealing compelling insights into the interplay among the non-commutative parameters $a^μ$ (with $|a^ν|$ being of the order of Planck length scale) and the speed of light $c$ as it approaches both infinity and zero. Our exploration predicts a sort of "branching" of the non-commutative parameters $a^μ$, leading to the emergence of a novel length scale and time scale in either limit. Furthermore, our investigation extends to the examination of curved momentum spaces and their geodesic distances in appropriate subspaces of the $κ$-deformed Newtonian and Carrollian space-times. We finally delve into the study of their deformed dispersion relations, arising from these deformed geodesic distances, providing a comprehensive understanding of the nature of these space-times. |
| title | Fate of $κ$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2401.05769 |