scholarly journals Thermal Casimir effect with general boundary conditions

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
J. M. Muñoz-Castañeda ◽  
L. Santamaría-Sanz ◽  
M. Donaire ◽  
M. Tello-Fraile
Keyword(s):  
Boundary Conditions ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
Quantum Field ◽  
Quantum Vacuum ◽  
Parallel Plates ◽  
Casimir Forces ◽  
Thermal Correction ◽  
Frequency Independent ◽  
Scalar Quantum

Abstract In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent boundary conditions that satisfy the conditions of isotropy and homogeneity and are compatible with the unitarity of the quantum field theory. Under these conditions we compute the thermal correction to the quantum vacuum energy as a function of the temperature and the parameters encoding the boundary condition. The latter enables us to obtain similar results for the pressure between plates and the quantum thermal correction to the entropy. We find out that our system is thermodynamically stable for any boundary conditions, and we identify a critical temperature below which certain boundary conditions yield attractive, repulsive, and null Casimir forces.

scholarly journals Casimir Effect in Domain Wall Formation

2003 ◽  
Vol 18 (23) ◽  
pp. 4285-4293 ◽  
Author(s):  
M. R. Setare
Keyword(s):  
Domain Wall ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Casimir Effect ◽  
Mixed Boundary Conditions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
De Sitter ◽  
Casimir Forces

The Casimir forces on two parallel plates in conformally flat de Sitter background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. Different cosmological constants are assumed for the space between and outside of the plates to have general results applicable to the case of domain wall formations in the early universe.

scholarly journals Fermionic Casimir effect in Horava–Lifshitz theories

2019 ◽  
Vol 34 (20) ◽  
pp. 1950107
Author(s):  
Dêivid R. da Silva ◽  
M. B. Cruz ◽  
E. R. Bezerra de Mello
Keyword(s):  
Boundary Condition ◽  
Casimir Effect ◽  
Lorentz Symmetry ◽  
Casimir Energy ◽  
Quantum Field ◽  
Parallel Plates ◽  
Symmetry Violation ◽  
Massless Quantum

In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava–Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.

scholarly journals Is the Free Vacuum Energy Infinite?

2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
H. Razmi ◽  
S. M. Shirazi
Keyword(s):  
Energy Density ◽  
Free Space ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
Fourth Power ◽  
Vacuum Energy Density ◽  
Uncertainty Relations ◽  
Quantum Vacuum ◽  
Cosmological Constant Problem ◽  
Virtual Particles

Considering the fundamental cutoff applied by the uncertainty relations’ limit on virtual particles’ frequency in the quantum vacuum, it is shown that the vacuum energy density is proportional to the inverse of the fourth power of the dimensional distance of the space under consideration and thus the corresponding vacuum energy automatically regularized to zero value for an infinitely large free space. This can be used in regularizing a number of unwanted infinities that happen in the Casimir effect, the cosmological constant problem, and so on without using already known mathematical (not so reasonable) techniques and tricks.

scholarly journals Some remarks on axion dark matter, dark energy and energy of the quantum vacuum

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040036
Author(s):  
V. M. Mostepanenko
Keyword(s):  
Field Theory ◽  
Dark Matter ◽  
Dark Energy ◽  
Cosmological Constant ◽  
Physical Significance ◽  
Quantum Field ◽  
Quantum Vacuum ◽  
Casimir Forces ◽  
Nucleon Interaction ◽  
The Difference

In connection with the problem of dark matter, we discuss recent results on constraining the parameters of axion-to-nucleon interaction following from the experiment on measuring the difference of Casimir forces. It is shown that this experiment not only leads to competitive constraints, but provides stronger support to other constraints obtained in Casimir physics so far. The description of dark energy by means of cosmological constant originated from the quantum vacuum is considered in terms of the renormalization procedures in quantum field theory. It is argued that only the renormalized value of cosmological constant directly connected with the observed density of dark energy is of physical significance, so that some statements in the literature concerning the vacuum catastrophe may be considered as an exaggeration.

Remarks on a gravitational analogue of the Casimir effect

2016 ◽  
Vol 25 (09) ◽  
pp. 1641018 ◽  
Author(s):  
V. B. Bezerra ◽  
H. F. Mota ◽  
C. R. Muniz
Keyword(s):  
Scalar Field ◽  
Cosmic String ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
String Tension ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Einstein Universe

We consider the Casimir effect, by calculating the Casimir energy and its corrections for nonzero temperatures, of a massless scalar field in the spacetime with topology [Formula: see text] (Einstein universe) containing an idealized cosmic string. The obtained results confirm the role played by the identifications imposed on the quantum field by boundary conditions arising from the topology of the gravitational field under consideration and illustrate a realization of a gravitational analogue of the Casimir effect. In this backgorund, we show that the vacuum energy can be written as a term which corresponds to the vacuum energy of the massless scalar field in the Einstein universe added by another term that formally corresponds to the vacuum energy of the electromagnetic field in the Einstein universe, multiplied by a parameter associated with the presence of the cosmic string, namely, [Formula: see text], where [Formula: see text] is a constant related to the cosmic string tension, [Formula: see text].

scholarly journals Perturbative Versus Non-Perturbative Quantum Field Theory: Tao’s Method, the Casimir Effect, and Interacting Wightman Theories

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 229
Author(s):  
Walter Felipe Wreszinski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Casimir Effect ◽  
Asymptotic Series ◽  
Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
Parallel Plates ◽  
Perturbative Approach ◽  
Usual Theory

We dwell upon certain points concerning the meaning of quantum field theory: the problems with the perturbative approach, and the question raised by ’t Hooft of the existence of the theory in a well-defined (rigorous) mathematical sense, as well as some of the few existent mathematically precise results on fully quantized field theories. Emphasis is brought on how the mathematical contributions help to elucidate or illuminate certain conceptual aspects of the theory when applied to real physical phenomena, in particular, the singular nature of quantum fields. In a first part, we present a comprehensive review of divergent versus asymptotic series, with qed as background example, as well as a method due to Terence Tao which conveys mathematical sense to divergent series. In a second part, we apply Tao’s method to the Casimir effect in its simplest form, consisting of perfectly conducting parallel plates, arguing that the usual theory, which makes use of the Euler-MacLaurin formula, still contains a residual infinity, which is eliminated in our approach. In the third part, we revisit the general theory of nonperturbative quantum fields, in the form of newly proposed (with Christian Jaekel) Wightman axioms for interacting field theories, with applications to “dressed” electrons in a theory with massless particles (such as qed), as well as unstable particles. Various problems (mostly open) are finally discussed in connection with concrete models.

scholarly journals On the Evaluation of Vacuum Energy Density in Quantum Field Theory

2021 ◽  
Author(s):  
Ervin Goldfain
Keyword(s):  
Energy Density ◽  
Vacuum Energy ◽  
Textbook Analysis ◽  
Harmonic Oscillators ◽  
Vacuum Energy Density ◽  
Model Parameters ◽  
Quantum Field ◽  
Quantum Vacuum ◽  
Flat Spacetime ◽  
The Standard Model

The textbook analysis of vacuum energy density (VED) in flat spacetime follows from Pauli’s lectures of 1951, in which quantum vacuum is modeled as a reservoir of free harmonic oscillators. In his lectures, Pauli shows that deriving a nearly vanishing VED is contingent upon fulfilling three corollary conditions called polynomial-in-mass-constraints. The goal of this work is to evaluate Pauli’s constraints against the Standard Model parameters and the Higgs mechanism of spontaneous symmetry breaking.

scholarly journals Casimir effect in Horava–Lifshitz-like theories

2015 ◽  
Vol 30 (36) ◽  
pp. 1550220 ◽  
Author(s):  
I. J. Morales Ulion ◽  
E. R. Bezerra de Mello ◽  
A. Yu. Petrov
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Casimir Force ◽  
Casimir Effect ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Scalar Field Theory

In this paper, we consider a Lorentz-breaking scalar field theory within the Horava–Lifshtz approach. We investigate the changes that a space–time anisotropy produces in the Casimir effect. A massless real quantum scalar field is considered in two distinct situations: between two parallel plates and inside a rectangular two-dimensional box. In both cases, we have adopted specific boundary conditions on the field at the boundary. As we shall see, the energy and the Casimir force strongly depends on the parameter associated with the breaking of Lorentz symmetry and also on the boundary conditions.

Recent progress in engineering the Casimir effect – applications to nanophotonics, nanomechanics, and chemistry

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 523-536
Author(s):  
Tao Gong ◽  
Matthew R. Corrado ◽  
Ahmed R. Mahbub ◽  
Calum Shelden ◽  
Jeremy N. Munday
Keyword(s):  
Quantum Mechanics ◽  
Boundary Conditions ◽  
Recent Progress ◽  
Casimir Effect ◽  
Classical Electrodynamics ◽  
Quantum Vacuum ◽  
Vacuum Fluctuations ◽  
Future Directions ◽  
Recent Developments ◽  
Repulsive Forces

AbstractQuantum optics combines classical electrodynamics with quantum mechanics to describe how light interacts with material on the nanoscale, and many of the tricks and techniques used in nanophotonics can be extended to this quantum realm. Specifically, quantum vacuum fluctuations of electromagnetic fields experience boundary conditions that can be tailored by the nanoscopic geometry and dielectric properties of the involved materials. These quantum fluctuations give rise to a plethora of phenomena ranging from spontaneous emission to the Casimir effect, which can all be controlled and manipulated by changing the boundary conditions for the fields. Here, we focus on several recent developments in modifying the Casimir effect and related phenomena, including the generation of torques and repulsive forces, creation of photons from vacuum, modified chemistry, and engineered material functionality, as well as future directions and applications for nanotechnology.

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