Symplectic Quantization and Minkowskian Statistical Mechanics: simulations on a 1+1 lattice
| Autor: | Giachello, Martina, Gradenigo, Giacomo, Scardino, Francesco |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | PoS(LATTICE2024)359 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.22323/1.466.0359 |
| Popis: | 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 $\tau$. In this framework, expectation values over quantum fluctuations are computed as dynamical averages along the trajectories parameterized by $\tau$. 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. Comment: 9 pages, 2 figures |
| Databáze: | arXiv |
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