A Novel Ansatz for the Energy-Momentum Tensor on the Lattice

TL;DR

This paper introduces a new lattice model for the symmetric energy-momentum tensor in pure Yang-Mills theory, using half powers of plaquette variables, and compares it with existing models through Monte Carlo simulations.

Contribution

It proposes a novel ansatz for the energy-momentum tensor on the lattice based on principal square roots of unitary matrices, aligning with thermodynamic principles.

Findings

Monte Carlo results support the new model's consistency

Comparison shows improvements over previous lattice models

Results favor a Wilson form for certain tensor components

Abstract

The comparison of structural analogies between the energy-momentum tensors in general relativity and in a gauge theory of Yang-Mills type is tentatively extended to lattice physics. These considerations are guiding to a new lattice model for the symmetric energy-momentum tensor $\Theta_{\mu\nu}$ of the pure Yang-Mills gauge sector, basing on half powers of the plaquette variable. The concept of non-trivial principal square roots of unitary matrices in lattice gauge theories can be epitomized to reconcile the pretension to a uniform construction principle for the components of $\Theta_{\mu\nu}$ with general qualitative thermodynamic demands concerning arguments in favour of a Wilson form for $<\Theta^\mu_\mu>$ and $\Theta_{44}$. SU(2) Monte Carlo results for the Euclidean expectation values on a 10**4 lattice are compared with that of competing hitherto existing lattice models for $\Theta_{\mu\nu}$.