Abstract
We propose a new strategy for determining the equation of state of a relativistic thermal quantum field theory by considering it in a moving reference system. In this frame, an observer can measure the entropy density of the system directly from its average total momentum. In the Euclidean path integral formalism, this amounts to computing the expectation value of the off-diagonal components of the energy-momentum tensor in the presence of shifted boundary conditions. The entropy is, thus, easily measured from the expectation value of a local observable computed at the target temperature only. At large , the temperature itself is the only scale which drives the systematic errors, and the lattice spacing can be tuned to perform a reliable continuum limit extrapolation while keeping finite-size effects under control. We test this strategy for the four-dimensional Yang-Mills theory. We present precise results for the entropy density and its step-scaling function in the temperature range . At each temperature, we consider four lattice spacings in order to extrapolate the results to the continuum limit. As a by-product, we also determine the ultraviolet finite renormalization constant of by imposing suitable Ward identities. These findings establish this strategy as a solid, simple, and efficient method for an accurate determination of the equation of state of a relativistic thermal field theory over several orders of magnitude in .
- Received 13 March 2014
DOI:https://doi.org/10.1103/PhysRevLett.113.031601
© 2014 American Physical Society