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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2308.01108 |
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| _version_ | 1866910292413251584 |
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| author | Nikjoo, Mehraveh Zlosnik, Tom |
| author_facet | Nikjoo, Mehraveh Zlosnik, Tom |
| contents | A number of approaches to gravitation have much in common with the gauge theories of the standard model of particle physics. In this paper, we develop the Hamiltonian formulation of a class of gravitational theories that may be regarded as spontaneously-broken gauge theories of the complexified Lorentz group $SO(1,3)_C$ with the gravitational field described entirely by a gauge field valued in the Lie algebra of $SO(1,3)_C$ and a `Higgs field' valued in the group's fundamental representation. The theories have one free parameter $β$ which appears in a similar role to the inverse of the Barbero-Immirzi parameter of Einstein-Cartan theory. However, contrary to that parameter, it is shown that the number of degrees of freedom crucially depends on the value of $β$. For non-zero values of $β$, it is shown that three complex degrees of freedom propagate on general backgrounds, and for the specific values $β=\pm i$ an extension to General Relativity is recovered in a symmetry-broken regime. For the value $β=0$, the theory propagates no local degrees of freedom. A non-zero value of $β$ corresponds to the self-dual and anti-self-dual gauge fields appearing asymmetrically in the action, therefore in these models, the existence of gravitational degrees of freedom is tied to chiral asymmetry in the gravitational sector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01108 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group Nikjoo, Mehraveh Zlosnik, Tom General Relativity and Quantum Cosmology A number of approaches to gravitation have much in common with the gauge theories of the standard model of particle physics. In this paper, we develop the Hamiltonian formulation of a class of gravitational theories that may be regarded as spontaneously-broken gauge theories of the complexified Lorentz group $SO(1,3)_C$ with the gravitational field described entirely by a gauge field valued in the Lie algebra of $SO(1,3)_C$ and a `Higgs field' valued in the group's fundamental representation. The theories have one free parameter $β$ which appears in a similar role to the inverse of the Barbero-Immirzi parameter of Einstein-Cartan theory. However, contrary to that parameter, it is shown that the number of degrees of freedom crucially depends on the value of $β$. For non-zero values of $β$, it is shown that three complex degrees of freedom propagate on general backgrounds, and for the specific values $β=\pm i$ an extension to General Relativity is recovered in a symmetry-broken regime. For the value $β=0$, the theory propagates no local degrees of freedom. A non-zero value of $β$ corresponds to the self-dual and anti-self-dual gauge fields appearing asymmetrically in the action, therefore in these models, the existence of gravitational degrees of freedom is tied to chiral asymmetry in the gravitational sector. |
| title | Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2308.01108 |