Mass Dependence of Vacuum Energy

Details Mass Dependence of Vacuum Energy Mass Dependence of Vacuum Energy

2005-07-05

arxiv.org/abs/math-ph/0507010v2

Phys.Lett. B624 (2005) 281-286

Physics

Mathematical Physics

8 pages, RevTeX; v.2 has minor updates and format changes

Scientific paper

10.1016/j.physletb.2005.08.040

The regularized vacuum energy (or energy density) of a quantum field subjected to static external conditions is shown to satisfy a certain partial differential equation with respect to two variables, the mass and the "time" (ultraviolet cutoff parameter). The equation is solved to provide integral expressions for the regularized energy (more precisely, the cylinder kernel) at positive mass in terms of that for zero mass. Alternatively, for fixed positive mass all coefficients in the short-time asymptotics of the regularized energy can be obtained recursively from the first nontrivial coefficient, which is the renormalized vacuum energy.

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