流形上经由相对谱不变量的Bogolyubov不变量
Bogolyubov invariant via relative spectral invariants on manifolds
摘要：
引入并研究了无边界紧致光滑流形上Laplace型和Dirac型两个椭圆型偏微分算子的谱不变量，该谱不变量依赖于算子的本征值和本征截面，当动力学算子依赖于时间时，它等于真空中产生粒子的正则化数目.我们研究了小绝热参数下这个不变量的渐近展开式，并明确地计算了渐近展开式的前两个系数。
英文摘要：
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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