Homological Quantum Mechanics
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866917586415910912 |
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| author | Chiaffrino, Christoph Hohm, Olaf Pinto, Allison F. |
| author_facet | Chiaffrino, Christoph Hohm, Olaf Pinto, Allison F. |
| contents | We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the harmonic oscillator to finite-dimensional phase space. This induces a homotopy transfer from the BV algebra to the algebra of functions on phase space. Quantum expectation values for a given operator or functional are computed by the function whose pullback gives a functional in the same cohomology class. This statement is proved in perturbation theory by relating the perturbation lemma to Wick's theorem. We test this method by computing two-point functions for the harmonic oscillator for position eigenstates and coherent states. Finally, we derive the Unruh effect, illustrating that these methods are applicable to quantum field theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_11495 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Homological Quantum Mechanics Chiaffrino, Christoph Hohm, Olaf Pinto, Allison F. High Energy Physics - Theory Mathematical Physics Quantum Physics We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the harmonic oscillator to finite-dimensional phase space. This induces a homotopy transfer from the BV algebra to the algebra of functions on phase space. Quantum expectation values for a given operator or functional are computed by the function whose pullback gives a functional in the same cohomology class. This statement is proved in perturbation theory by relating the perturbation lemma to Wick's theorem. We test this method by computing two-point functions for the harmonic oscillator for position eigenstates and coherent states. Finally, we derive the Unruh effect, illustrating that these methods are applicable to quantum field theory. |
| title | Homological Quantum Mechanics |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2112.11495 |