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

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 $\Theta_{\mu\nu}$.