Quantum Principle of Least Action in Dynamic Theories With Higher Derivatives
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929313933164544 |
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| author | Gorobey, Natalia Lukyanenko, Alexander Goltsev, A. V. |
| author_facet | Gorobey, Natalia Lukyanenko, Alexander Goltsev, A. V. |
| contents | A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory, in which the state of motion of the system is described by the wave functional on its trajectories in the configuration space, and the functional itself is an eigenvector of the action operator. The Pais-Uhlenbeck oscillator is considered as the simplest model. For this case, the correspondence between the new form of quantum theory and "ordinary" quantum mechanics has been established in the local limit, when the Pais-Uhlenbeck oscillator is reduced to the "ordinary" harmonic oscillator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09608 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Principle of Least Action in Dynamic Theories With Higher Derivatives Gorobey, Natalia Lukyanenko, Alexander Goltsev, A. V. Quantum Physics A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory, in which the state of motion of the system is described by the wave functional on its trajectories in the configuration space, and the functional itself is an eigenvector of the action operator. The Pais-Uhlenbeck oscillator is considered as the simplest model. For this case, the correspondence between the new form of quantum theory and "ordinary" quantum mechanics has been established in the local limit, when the Pais-Uhlenbeck oscillator is reduced to the "ordinary" harmonic oscillator. |
| title | Quantum Principle of Least Action in Dynamic Theories With Higher Derivatives |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.09608 |