Symplectic Quantization and Minkowskian Statistical Mechanics: simulations on a 1+1 lattice
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917964305924096 |
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| author | Giachello, Martina Gradenigo, Giacomo Scardino, Francesco |
| author_facet | Giachello, Martina Gradenigo, Giacomo Scardino, Francesco |
| contents | We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols, well defined only for Euclidean Field Theory. This importance sampling procedure is realized by means of a deterministic dynamics generated by Hamilton-like equations evolving with respect to an auxiliary time parameter $τ$. In this framework, expectation values over quantum fluctuations are computed as dynamical averages along the trajectories parameterized by $τ$. Assuming ergodicity, this is equivalent to sample a microcanonical partition function. Then, by means of a large-M calculation, where M is the number of degrees of freedom on the lattice, we show that the microcanonical correlation functions are equivalent to those generated by a Minkowskian canonical theory where quantum fields fluctuations are weighted by the factor $\exp(S/\hbar )$, with $S$ being the original relativistic action of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symplectic Quantization and Minkowskian Statistical Mechanics: simulations on a 1+1 lattice Giachello, Martina Gradenigo, Giacomo Scardino, Francesco High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Theory We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols, well defined only for Euclidean Field Theory. This importance sampling procedure is realized by means of a deterministic dynamics generated by Hamilton-like equations evolving with respect to an auxiliary time parameter $τ$. In this framework, expectation values over quantum fluctuations are computed as dynamical averages along the trajectories parameterized by $τ$. Assuming ergodicity, this is equivalent to sample a microcanonical partition function. Then, by means of a large-M calculation, where M is the number of degrees of freedom on the lattice, we show that the microcanonical correlation functions are equivalent to those generated by a Minkowskian canonical theory where quantum fields fluctuations are weighted by the factor $\exp(S/\hbar )$, with $S$ being the original relativistic action of the system. |
| title | Symplectic Quantization and Minkowskian Statistical Mechanics: simulations on a 1+1 lattice |
| topic | High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.09162 |