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We propose a thermodynamical definition of the vacuum energy density ₕ₀₂, defined as 0| T_ |0 = - ₕ₀₂ \, g_, 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 = 1/T 0. It takes the form ₕ₀₂ = const mD where m is a fundamental mass scale and "const" is a computable constant which can be positive or negative. Due to modular invariance ₕ₀₂ can also be computed in a different non-thermodynamic channel where one spatial dimension is compactifed on a circle of circumference and we confirm this modularity for free massive theories for both bosons and fermions for D=2, 3, 4. We list various properties of ₕ₀₂ that are generally required, for instance ₕ₀₂=0 for conformal field theories, and others, such as the constraint that ₕ₀₂ 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 ₕ₀₂ exactly for 2 classes of integrable QFT's in 2D and interpreting some previously known results. We apply our definition of ₕ₀₂ to Lattice QCD data with two light quarks (up and down) and one additional massive flavor (the strange quark), and find it is negative, ₕ₀₂ - (200 \, MeV) ⁴. Finally we make some remarks on the Cosmological Constant Problem since ₕ₀₂ is central to any discussion of it.
André LeClair (Tue,) studied this question.