Thermodynamic formulation of vacuum energy density in flat spacetime and potential implications for the cosmological constant

We propose a thermodynamical definition of the vacuum energy density rho vac, defined as < vac|T mu nu|vac > = - rho vacg mu nu, in quantum field theory in flat Minkowski space in D spacetime dimensions, which can be computed in the limit of high temperature, namely in the limit beta = 1/T -> 0. It takes the form rho vac = const center dot mD where m is a fundamental mass scale and "const" is a computable constant which can be positive or negative depending on interaction couplings. Due to modular invariance rho vac can also be computed in a different non-thermodynamic channel where one spatial dimension is compactifed on a circle of circumference beta and we confirm this modularity for free massive theories for both bosons and fermions for D = 2, 3, 4. We list various properties of rho vac that are generally required, for instance rho vac = 0 for conformal field theories, and others, such as the constraint that rho vac has opposite signs for free bosons verses fermions of the same mass, which is related to constraints from supersymmetry. Using the Thermodynamic Bethe Ansatz we compute rho vac exactly for 2 classes of integrable QFT's in 2D and interpreting some previously known results. We apply our definition of rho vac to Lattice QCD data with two light quarks (up and down) and one additional massive flavor (the strange quark), and find it is negative, rho vac approximate to - (200 MeV)4. Finally we make some remarks on the Cosmological Constant Problem since rho vac is central to any discussion of it.