New two-operator heat trace invariants are defined and their first two short-time asymptotic coefficients are computed explicitly.
Bogolyubov invariant via relative spectral invariants on manifolds
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abstract
We introduce and study new spectral invariant of two elliptic partial differential operators of Laplace and Dirac type on compact smooth manifolds without boundary that depends on both the eigenvalues and the eigensections of the operators, which is a equal to the regularized number of created particles from the vacuum when the dynamical operator depends on time. We study the asymptotic expansion of this invariant for small adiabatic parameter and compute explicitly the first two coefficients of the asymptotic expansion.
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Relative Spectral Invariants of Elliptic Operators on Manifolds
New two-operator heat trace invariants are defined and their first two short-time asymptotic coefficients are computed explicitly.