Energy Density and Pressure in Power-Wall Models

Fulling, S. A.; Milton, Kimball A.; Wagner, Jef

doi:10.1142/s2010194512007271

Cited by 2 publications

(3 citation statements)

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“…(2.13b) and (2.13c). This proves the nonexistence of a transverse pressure anomaly [13], completing the argument in Ref. [11].…”

Section: Renormalizationsupporting

confidence: 81%

“…The problem of justifying that step physically by a genuine renormalization of coupling constants in a full theory including the gravitational field and the scalar field v as dynamical objects will not be discussed here (but see Refs. [9,12,13]), hence our use of quotation marks around "renormalized". Another problem, however, cannot be postponed: It is impossible to separate logarithmically divergent terms from finite terms in a scale-invariant manner, and likewise it is impossible to separate direction-dependent terms from directionindependent finite terms unambiguously.…”

Section: Renormalizationmentioning

confidence: 99%

“…III are systematically discarded in Sec. V. As in the curved-space analogue, at least some of these divergences correspond to terms in the original Lagrangian [9,12,13], so we shall refer to this process as "renormalization." There are logarithmically divergent terms; these transform into finite terms depending logarithmically on the potential with an arbitrary mass scale.…”

Section: Introductionmentioning

confidence: 99%

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Stress tensor for a scalar field in a spatially varying background potential: Divergences, “renormalization”, anomalies, and Casimir forces

et al. 2016

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Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporalspatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth-and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for z < 0 and rises like z α , α > 0, for z > 0. Previously, the stress tensor had been computed outside of the wall, whereas now we compute all components of the stress tensor in the interior of the wall. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, α = 1 and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).

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“…(2.13b) and (2.13c). This proves the nonexistence of a transverse pressure anomaly [13], completing the argument in Ref. [11].…”

Section: Renormalizationsupporting

confidence: 81%

Section: Renormalizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stress tensor for a scalar field in a spatially varying background potential: Divergences, “renormalization”, anomalies, and Casimir forces

et al. 2016

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Local Casimir Effect for a Scalar Field in Presence of a Point Impurity

Fermi

Pizzocchero

2018

Symmetry

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Abstract:The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini have considered some configurations involving delta-type potentials concentrated at points of R 3 ; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on R 3 \{0}, with self-adjoint boundary conditions at the origin for the Laplacian. However, the above authors have discussed only global aspects of the Casimir effect, focusing their attention on the vacuum expectation value (VEV) of the total energy. In the present paper we analyze the local Casimir effect with a point delta-type potential, computing the renormalized VEV of the stress-energy tensor at any point of R 3 \{0}; for this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours.

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Energy Density and Pressure in Power-Wall Models

Cited by 2 publications

References 23 publications

Stress tensor for a scalar field in a spatially varying background potential: Divergences, “renormalization”, anomalies, and Casimir forces

Stress tensor for a scalar field in a spatially varying background potential: Divergences, “renormalization”, anomalies, and Casimir forces

Local Casimir Effect for a Scalar Field in Presence of a Point Impurity

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