High Energy / Nuclear Theory / RIKEN Seminars

[Hybrid RBRC seminar] Discussions regarding the real-time path integral of lattice gauge theories

by Nobuyuki Matsumoto (RIKEN)

2-160 (https://bnl.zoomgov.com/j/1606067399?pwd=am02b0xIUXZ6TDR3d1dWL05TTDdaUT09)

2-160 (https://bnl.zoomgov.com/j/1606067399?pwd=am02b0xIUXZ6TDR3d1dWL05TTDdaUT09)


The interest in real-time dynamics has been increasing not only from the accumulating experimental data, e.g. of heavy-ion collisions, but also from the theoretical developments such as algorithms for the sign problem as well as quantum computing. It is therefore becoming of practical importance how we should define the real-time path integrals constructively and evaluate them non-perturbatively. While the conventional lattice formulation of gauge theories uses compact link variables, it has been discussed that the real-time path integral of compact variables needs special care [1,2,3]. In this talk, I will clarify how the subtlety arises for the Wilson action of continuous gauge groups in the continuum limit [4]. A simple prescription will be to introduce the i epsilon, which however would enforce us to break unitarity on the lattice. I would like to informally discuss related problems and a possible consequence on quantum computing.

[1] W. Langguth and A. Inomata, "Remarks on the Hamiltonian path integral in polar coordinates," J. Math. Phys. 20, 499-504 (1979).
[2] H. Hoshina, H. Fujii and Y. Kikukawa, “Schwinger-Keldysh formalism for Lattice Gauge Theories," PoS LATTICE2019, 190 (2020).
[3] G. Kanwar and M. L. Wagman, "Real-time lattice gauge theory actions: Unitarity, convergence, and path integral contour deformations," Phys. Rev. D 104, no.1, 014513 (2021) [arXiv:2103.02602 [hep-lat]].
[4] NM, "Comment on the subtlety of defining a real-time path integral in lattice gauge theories," PTEP 2022 (2022) no.9, 093B03 [arXiv:2206.00865 [hep-lat]].

Organized by

Nobuyuki Matsumoto