Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels

@inproceedings{Fermi2017LocalZR,
  title={Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels},
  author={Davide Fermi and L. Pizzocchero},
  year={2017}
}
This is the first one of a series of papers about zeta regularization of the divergences appearing in the vacuum expectation value (VEV) of several local and global observables in quantum field theory. More precisely we consider a quantized, neutral scalar field on a domain in any spatial dimension, with arbitrary boundary conditions and, possibly, in presence of an external classical potential. We analyze, in particular, the VEV of the stress-energy tensor, the corresponding boundary forces… Expand
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Local zeta regularization and the scalar Casimir effect II. Some explicitly solvable cases
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Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we compute the renormalized vacuum expectation value of several observables (in particular,… Expand
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Local Casimir Effect for a Scalar Field in Presence of a Point Impurity
TLDR
The local Casimir effect with a point delta-type potential is analyzed, computing the renormalized VEV of the stress-energy tensor at any point of $\mathbb{R}^3\setminus \mathbf{0}\}$; to this purpose the zeta regularization approach is followed, in the formulation already employed for different configurations in previous works of the authors'. Expand
Algebraic Approach to Casimir Force Between Two $$\delta $$-like Potentials
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Integrating Gauge Fields in the $\zeta$-formulation of Feynman's path integral
In recent work by the authors, a connection between Feynman’s path integral and Fourier integral operator ζ-functions has been established as a means of regularizing the vacuum expectation values in… Expand
Integrating Gauge Fields in the ζ-Formulation of Feynman’s Path Integral
In recent work by the authors, a connection between Feynman’s path integral and Fourier integral operator ζ-functions has been established as a means of regularizing the vacuum expectation values in… Expand
Relative-Zeta and Casimir Energy for a Semitransparent Hyperplane Selecting Transverse Modes
We study the relative zeta function for the couple of operators A0 and A α , where A0 is the free unconstrained Laplacian in L2(R d ) (d ≥ 2) and A α is the singular perturbation of A0 associated to… Expand
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A pr 2 02 1 A note on “ Algebraic approach to Casimir force between two δ-like potentials ” (
We comment on the recent work [1], and on its relations with our papers [2, 3] cited therein. In particular we show that, contrarily to what stated in [1], the Casimir energy density determined… Expand
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Local zeta regularization and the scalar Casimir effect II. Some explicitly solvable cases
In Part I of this series of papers we have described a general formalism to compute the vacuum effects of a scalar field via local (or global) zeta regularization. In the present Part II we exemplify… Expand
Local zeta regularization and the scalar Casimir effect IV. The case of a rectangular box
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