https://doi.org/10.1051/epjconf/202431400028
Symplectic quantization: A new deterministic approach to the dynamics of quantum fields inspired by statistical mechanics*
1 Gran Sasso Science Institute, Viale F. Crispi 7, 67100 L’Aquila, Italy
2 INFN-Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, 67100 Assergi (AQ), Italy
* Presented by M.Giachello at QCD@Work, 18 - 21 June 2024, Trani, Italy
** e-mail: martina.giachello@gssi.it
*** e-mail: giacomo.gradenigo@gssi.it
Published online: 10 December 2024
In this contribution we summarize the main features of a new algorithm (already presented in [1]) to sample numerically on the lattice the quantum fluctuations of fields by means of a deterministic pseudo-Hamiltonian dynamics in an enlarge space of variables. The main goal is to provide a numerical tool which is well defined in Minkowski space. The proposed approach introduces an additional time variable that plays the role of a true physical parameter that controls the deterministic dynamics. The sampling of quantum fluctuations is guaranteed by the presence of new additional conjugated momenta, which represent the rate of variation of ordinary fields with respect to the newly added time variable. From the pseudo-Hamiltonian dynamics one is then able, assuming ergodicity, to retrieve the Feynman path integral as the Fourier transform of a pseudo-microcanonical partition function.
© The Authors, published by EDP Sciences, 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
