We present a new mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in odd dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher dimensions. Remarkably, the regularization parameters can be computed in closed form in arbitrary dimensions and for arbitrary metric function $f(r)$. In fact, we show that in spite of the increasing severity and number of the divergences to be regularized, the method presented is mostly agnostic to the number of dimensions. Finally, as an explicit example of our method, we show plots for vacuum polarization in the Schwarzschild-Tangherlini spacetime for odd $d=5,...,11$.
Boundary Completion of Vacuum Persistence Probability
Beihang University（北京航空航天大学）；Center for Gravitational Physics, Department of Space Science, Beihang University（北京航空航天大学空间科学学院引力物理中心）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭桓武院系合作教育研究中心）
We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbit…
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In-In perturbation theory is a vital tool for cosmology and nonequilibrium physics. Here, we reconcile an apparent conflict between two of its important aspects with particular relevance to De Sitter/inflationary contexts: (i) the need to slightly deform unitary time evolution with an i*epsilon prescription that projects the free ("Bunch-Davies") vacuum onto the interacting vacuum and renders vertex integrals well-defined, and (ii) Weinberg's "nested commutator" reformulation of in-in perturbation theory which makes manifest the constraints of causality within expectation values of local opera…
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In this note, we consider the response of a uniformly accelerated monopole detector that is coupled non-linearly to the nth power of a quantum scalar field in (D+1)-dimensional flat spacetime. We show that, when (D+1) is even, the response of the detector in the Minkowski vacuum is characterized by a Bose-Einstein factor for all n. Whereas, when (D+1) is odd, we find that a Fermi-Dirac factor appears in the detector response when n is odd, but a Bose-Einstein factor arises when n is even.
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We consider the response of a uniformly accelerated monopole detector that is coupled non-linearly to the nth power of a quantum scalar field in (D+1)-dimensional flat spacetime. We show that, when (D+1) is even, the response of the detector in the Minkowski vacuum is characterized by a Bose-Einstein factor for all n. Whereas, when (D+1) is odd, we find that a Fermi-Dirac factor appears in the detector response when n is odd, but a Bose-Einstein factor arises when n is even. We emphasize the point that, since, along the accelerated trajectory, the Wightman function and, as a result, the (2n)-p…
The regularized vacuum fluctuation related to a conformally coupled massless scalar field defined on a space-time with dynamical horizon is computed with respect a radially moving observer in a generic flat Friedmann-Robertson-Walker space-time. Two simple measurement prescriptions are given in order to remove the ambiguity associated with the short distance singularity of the correlation function. In some cases, it turns out that one is dealing with a quantum thermometer, recovering a proposal due to Buchholzet al. in order to determine local temperature in the framework of quantum field theo…
We consider the response of a uniformly accelerated monopole detector that is coupled to a superposition of an odd and an even power of a quantized, massless scalar field in flat spacetime in arbitrary dimensions. We show that, when the field is assumed to be in the Minkowski vacuum, the response of the detector is characterized by a Bose-Einstein factor in even spacetime dimensions, whereas a Bose-Einstein as well as a Fermi-Dirac factor appear in the detector response when the dimension of spacetime is odd. Moreover, we find that, it is possible to interpolate between the Bose-Einstein and t…
