Thermal field theories and shifted boundary conditions

The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincaré invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L0 and the shift ξ only through the combination β = L0(1+ξ2)1/2. This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set ofWard identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: They offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedure.