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arXiv 1204.3262hep-thgr-qcmath-phmath.MP
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调零模式、规范固定、单频仪、$ζ$功能等

Zero modes, gauge fixing, monodromies, $ζ$-functions and all that

A. O. Barvinsky, D. V. Nesterov

备注：
17 pages, to appear in J. Phys. A: Math. Theor. arXiv admin note: substantial text overlap with arXiv:1111.4474
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摘要：

讨论了一类特殊的二阶微分算子$\boldmath$ {F} $ =-d^2/dτ^2+\ddot g/g$，$\ddot g\equiv d^2g/dτ^2$的约化泛函行列式的计算问题，该算子具有一般的函数$g(τ)$，且满足周期边界条件和Dirichlet边界条件.这些问题包括该行列式的规范固定路径积分表示、其计算的单值方法以及用于推导其周期依赖性的热核和zeta函数技术的组合。这个特殊的问题，来自量子宇宙学的应用的动机，也简要讨论。这些问题包括共形场论驱动下的宇宙学微正则初始条件问题、宇宙学常数问题和宇宙微波背景问题。

英文摘要：

We discuss various issues associated with the calculation of the reduced functional determinant of a special second order differential operator $\boldmath${F}$ =-d^2/dτ^2+\ddot g/g$, $\ddot g\equiv d^2g/dτ^2$, with a generic function $g(τ)$, subject to periodic and Dirichlet boundary conditions. These issues include the gauge-fixed path integral representation of this determinant, the monodromy method of its calculation and the combination of the heat kernel and zeta-function technique for the derivation of its period dependence. Motivations for this particular problem, coming from applications in quantum cosmology, are also briefly discussed. They include the problem of microcanonical initial conditions in cosmology driven by a conformal field theory, cosmological constant and cosmic microwave background problems.

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