Abstract
The Wilson action for Euclidean lattice gauge theory defines a positive-definite transfer matrix that corresponds to a unitary lattice gauge theory time-evolution operator if analytically continued to real time. Hoshina, Fujii, and Kikukawa (HFK) recently pointed out that applying the Wilson action discretization to continuum real-time gauge theory does not lead to this, or any other, unitary theory and proposed an alternate real-time lattice gauge theory action that does result in a unitary real-time transfer matrix. The character expansion defining the HFK action is divergent, and in this work we apply a path integral contour deformation to obtain a convergent representation for $U(1)$ HFK path integrals suitable for numerical Monte Carlo calculations. We also introduce a class of real-time lattice gauge theory actions based on analytic continuation of the Euclidean heat-kernel action. Similar divergent sums are involved in defining these actions, but for one action in this class this divergence takes a particularly simple form, allowing construction of a path integral contour deformation that provides absolutely convergent representations for $U(1)$ and $SU(N)$ real-time lattice gauge theory path integrals. We perform proof-of-principle Monte Carlo calculations of real-time $U(1)$ and $SU(3)$ lattice gauge theory and verify that exact results for unitary time evolution of static quark-antiquark pairs in ($1+1$)D are reproduced.
Highlights
Lattice quantum field theory methods have long been used to calculate equilibrium properties of strongly coupled quantum systems
Lattice gauge theory (LGT) in particular allows observables to be computed in strongly coupled gauge theories, for example including observables in quantum chromodynamics (QCD) that are relevant for understanding the dynamics of the strong force in the Standard Model
The lattice spacing is a free parameter that is independent of the gauge field coupling, rather than a dynamical quantity whose value in physical units must be determined by tuning the gauge coupling, as described, for example, in Ref. [37]
Summary
Lattice quantum field theory methods have long been used to calculate equilibrium properties of strongly coupled quantum systems. The summations defining the HK and HK actions are divergent, but a simple path integral contour is shown to provide an absolutely convergent representation of the HK action for Uð1Þ and SUðNÞ gauge theory in Minkowski spacetime with any dimension This is achieved using a prescription similar to the one applied for the HFK action: parametrizing a “Wick rotation” of the kinetic term prefactor, exactly canceling pieces of the deformed contour related by symmetry, and analytically taking the limit to prefactor i. The real-time Wilson action is not suitable for quantum LGT, the derived equations of motion do give well-defined deterministic evolution of the fields involved and result in a well-formed classical theory In these approaches, the lattice spacing is a free parameter that is independent of the gauge field coupling, rather than a dynamical quantity whose value in physical units must be determined by tuning the gauge coupling, as described, for example, in Ref.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
