We study the Casimir effect in the presence of an extra dimension compactified on a circle of radius R ($M^4\times S^1$ spacetime). Our starting point is the Kaluza Klein decomposition of the 5D Maxwell action into a massless sector containing the 4D Maxwell action and an extra massless scalar field and a Proca sector containing 4D gauge fields with masses $m_n=n/R$ where $n$ is a positive integer. An important point is that, in the presence of perfectly conducting parallel plates, the three degrees of freedom do not yield three discrete (non-penetrating) modes but two discrete modes and one continuum (penetrating) mode. The massless sector reproduces Casimir's original result and the Proca sector yields the corrections. The contribution from the Proca continuum mode is obtained within the framework of Lifshitz theory for plane parallel dielectrics whereas the discrete modes are calculated via 5D formulas for the piston geometry. An interesting manifestation of the extra compact dimension is that the Casimir force between perfectly conducting plates depends on the thicknesses of the slabs.
We discuss Stueckelberg massive electromagnetism on an arbitrary four-dimensional curved spacetime (gauge invariance of the classical theory and covariant quantization, wave equations for the massive spin-1 field $A_μ$, for the auxiliary Stueckelberg scalar field $Φ$ and for the ghost fields $C$ and $C^\ast$, Ward identities, Hadamard representation of the various Feynman propagators and covariant Taylor series expansions of the corresponding coefficients). This permits us to construct, for a Hadamard quantum state, the expectation value of the renormalized stress-energy tensor associated with…
We prove that vector fields described by the generalized Proca class of theories do not admit a consistent coupling to a gravitational sector defined by a scalar-tensor theory of the degenerate type. Under the assumption that there exists a frame in which the Proca field interacts with gravity only through the metric tensor, our analysis shows that at least one of the constraints associated with the degeneracy of the scalar-tensor sector is inevitably lost whenever the vector theory includes a coupling to the Christoffel connection.
Using the statistical description common to random waves and quantum fields we show how the probability of having a nodal line close to a (translationally symmetric) reference curve $γ$ is related to the Casimir energy of an appropriate configuration of conductors.
We discuss four different, though related, fundamental topics related to the Casimir effect: 1) We suggest that the application of Casimir theory to real dielectric materials, thus implying the atomic spacing as a course-grained length parameter, makes it natural to assume that this parameter is of the same order of magnitude as the QFT time-splitting parameter multiplied with the velocity of light. 2) We show that application of Casimir theory to a thick fluid shell (apparently a closed mechanical system), leads actually to an unstable situation if not extra mechanical forces, typically surfa…
We study the Casimir effect due to a massive vector field in a system of two parallel plates made of real materials, in an arbitrary magnetodielectric background. The plane waves satisfying the Proca equations are classified into transverse modes and longitudinal modes which have different dispersion relations. Transverse modes are further divided into type I and type II corresponding to TE and TM modes in the massless case. For general magnetodielectric media, we argue that the correct boundary conditions are the continuities of $\mathbf{H}_{\parallel}, ϕ, \mathbf{A}$ and $\pa_xA_x$, where $x…
We study the connection between $ζ$- and cutoff-regularized Casimir energies for scalar fields. We show that, in general, both regularization schemes lead to divergent contributions, and to finite parts which do not coincide. We determine the relationships among the various coefficients appearing in one approach and the other. As an application, we discuss the case of scalar fields in $d$-dimensional boxes under periodic boundary conditions.
We study cut-and-join operators for spin Hurwitz partition functions. We provide explicit expressions for these operators in terms of derivatives in $p$-variables without straightforward matrix realization, which is yet to be found. With the help of these expressions spin cut-and-join operators can be calculated directly and algorithmically. The reason why it is possible is the connection between mentioned operators and specially chosen Casimir operators that are easy to compute. An essential part of the connection involves shifted Q-Schur functions.
We study the field theoretical model of a scalar field in presence of spacial inhomogeneities in form of one and two finite width mirrors (material slabs). The interaction of the scalar field with the defect is described with position-dependent mass term. For the single layer system we develop a rigorous calculation method and derive explicitly the propagator of the theory, S-matrix elements and the Casimir self-energy of the slab. Detailed investigation of particular limits of self-energy is presented, and connection to know cases is discussed. The calculation method is found applicable to th…
The aim of this work is to investigate the role played by the fermion mass and that of an external field on the fermionic Casimir energy density under S^1 X R^3 topology. Both twisted and untwisted spin connections are considered and the exact calculation is performed using a somewhat different approach based on the combination of the analytic regularization method through alpha-representation and Euler-Maclaurin summation formula.
Zero-point fluctuations in quantum fields give rise to observable forces between material bodies, the so-called Casimir forces. In this lecture I present some results of the theory of the Casimir effect, primarily formulated in terms of Green's functions. There is an intimate relation between the Casimir effect and van der Waals forces. Applications to conductors and dielectric bodies of various shapes will be given for the cases of scalar, electromagnetic, and fermionic fields. The dimensional dependence of the effect will be described. Finally, we ask the question: Is there a connection betw…
Zero-point fluctuations in quantum fields give rise to observable forces between material bodies, the so-called Casimir forces. In these lectures I present the theory of the Casimir effect, primarily formulated in terms of Green's functions. There is an intimate relation between the Casimir effect and van der Waals forces. Applications to conductors and dielectric bodies of various shapes will be given for the cases of scalar, electromagnetic, and fermionic fields. The dimensional dependence of the effect will be described. Finally, we ask the question: Is there a connection between the Casimi…
We present a three-dimensional metric affine theory of gravity whose field equations lead to a connection introduced by Schrödinger many decades ago. Although involving nonmetricity, the Schrödinger connection preserves the length of vectors under parallel transport, and appears thus to be more physical than the one proposed by Weyl. By considering solutions with constant scalar curvature, we obtain a self-duality relation for the nonmetricity vector which implies a Proca equation that may also be interpreted in terms of inhomogeneous Maxwell equations emerging from affine geometry.
We investigate the connection between the entanglement system in Minkowski spacetime and the black hole using the scaling analysis. Here we show that the entanglement system satisfies the Bekenstein entropy bound. Even though the entropies of two systems are the same form, the entanglement energy is different from the black hole energy. Introducing the Casimir energy of the vacuum energy fluctuations rather than the entanglement energy, it shows a feature of the black hole energy. Hence the Casimir energy is more close to the black hole than the entanglement energy. Finally, we find that the e…
Julian Schwinger became interested in the Casimir effect in 1975. His original impetus was to understand the quantum force between parallel plates without the concept of zero point fluctuations of field quanta, in the language of source theory. He went on to consider applications to dielectrics and to spherical geometries in 1977. Although he published nothing on the subject in the following decade, he did devote considerable effort to understanding the connection between acceleration and temperature in the mid 1980s. During the last four years of his life, he became fascinated with sonolumine…
In our five-dimensional cosmological model, we investigate the role of a Lorentz violating vector "æther" field on the moduli stabilization mechanism. We consider the case of a space-like æther field on a compact circle with Maxwell-type kinetic term. The Casimir energy of certain combinations of massless and massive bulk fields generates a stabilizing potential for the radius of the compact direction while driving the accelerated expansion in the non-compact directions. It is shown that the æther field can reduce the influence of the Casimir force and slow down the oscillation of the radion f…
We propose a lower limit on the size of a single discrete gravitational extra dimension in the context of an effective field theory for massive gravitons. The limit arises in this setup from the requirement that the Casimir energy density of quantum fields is in agreement with the observed dark energy density of the universe. The Casimir energy densities can be exponentially suppressed to an almost arbitrarily small value by the masses of heavy bulk fields, thereby allowing a tiny size of the extra dimension. This suppression is only restricted by the strong coupling scale of the theory, which…
We propose a new table-top experimental configuration for the direct detection of dark matter axions with mass in the $(10^{-6} \rm eV - 10^{-2} \rm eV)$ range using non-perturbative effects in a system with non-trivial spatial topology. Different from most experimental setups found in literature on direct dark matter axion detection, which relies on $\dotθ$ or $\vec{\nabla}θ$, we found that our system is in principle sensitive to a static $θ\geq 10^{-14}$ and can also be used to set limit on the fundamental constant $θ_{\rm QED}$ which becomes the fundamental observable parameter of the Maxwe…
