The vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with Dirichlet boundary conditions and for the electromagnetic field inside a wedge with a coaxial cylindrical boundary. In the case of the electromagnetic field perfectly conducting boundary conditions are assumed on the bounding surfaces. By using the Abel-Plana-type formula for the series over the zeros of the Bessel function, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry without a cylindrical boundary and the second one is induced by the presence of the cylindrical shell. The additional vacuum forces acting on the wedge sides due the presence of the cylindrical boundary are evaluated and it is shown that these forces are attractive for both scalar and electromagnetic fields.
The torque density per unit height exerted on a perfectly conducting wedge due to the quantum vacuum fluctuations (the Casimir torque) is obtained. A canonical quantum field theoretical approach with the method of calculating vacuum-to-vacuum propagator (Green function) [1] is used.
Various applications of the multiple scattering technique to calculating Casimir energy are described. These include the interaction between dilute bodies of various sizes and shapes, temperature dependence, interactions with multilayered and corrugated bodies, and new examples of exactly solvable separable bodies.
We consider the Casimir energy due to a massless scalar field in a geometry of an infinite wedge closed by a Dirichlet circular cylinder, where the wedge is formed by $δ$-function potentials, so-called semitransparent boundaries. A finite expression for the Casimir energy corresponding to the arc and the presence of both semitransparent potentials is obtained, from which the torque on the sidewalls can be derived. The most interesting part of the calculation is the nontrivial nature of the angular mode functions. Numerical results are obtained which are closely analogous to those recently foun…
We consider the Casimir energy in a geometry of an infinite magnetodielectric wedge closed by a circularly cylindrical, perfectly conducting arc embedded in another magnetodielectric medium, under the condition that the speed of light be the same in both media. An expression for the Casimir energy corresponding to the arc is obtained and it is found that in the limit where the reflectivity of the wedge boundaries tends to unity the finite part of the Casimir energy of a perfectly conducting wedge-shaped sheet closed by a circular cylinder is regained. The energy of the latter geometry possesse…
We consider the Casimir-Helmholtz free energy at nonzero temperature $T$ for a circular cylinder and perfectly conducting wedge closed by a cylindrical arc, either perfectly conducting or isorefractive. The energy expression at nonzero temperature may be regularized to obtain a finite value, except for a singular corner term in the case of the wedge which is present also at zero temperature. Assuming the medium in the interior of the cylinder or wedge be nondispersive with refractive index $n$, the temperature dependence enters only through the non-dimensional parameter $2πnaT$, $a$ being the …
The wedge geometry closed by a circular-cylindrical arc is a nontrivial generalization of the cylinder, which may have various applications. If the radial boundaries are not perfect conductors, the angular eigenvalues are only implicitly determined. When the speed of light is the same on both sides of the wedge, the Casimir energy is finite, unlike the case of a perfect conductor, where there is a divergence associated with the corners where the radial planes meet the circular arc. We advance the study of this system by reporting results on the temperature dependence for the conducting situati…
Although repulsive effects have been predicted for quantum vacuum forces between bodies with nontrivial electromagnetic properties, such as between a perfect electric conductor and a perfect magnetic conductor, realistic repulsion seems difficult to achieve. Repulsion is possible if the medium between the bodies has a permittivity in value intermediate to those of the two bodies, but this may not be a useful configuration. Here, inspired by recent numerical work, we initiate analytic calculations of the Casimir-Polder interaction between an atom with anisotropic polarizability and a plate with…
In this paper we study an archetypical scenario in which repulsive Casimir-Polder forces between an atom or molecule and two macroscopic bodies can be achieved. This is an extension of previous studies of the interaction between a polarizable atom and a wedge, in which repulsion occurs if the atom is sufficiently anisotropic and close enough to the symmetry plane of the wedge. A similar repulsion occurs if such an atom passes a thin cylinder or a wire. An obvious extension is to compute the interaction between such an atom and two facing wedges, which includes as a special case the interaction…
The vacuum energy density of electromagnetic field inside a perfectly conducting wedge is calculated by making use of the local zeta function technique. This regularization completely eliminates divergent expressions in the course of calculations and gives rise to a finite expression for the energy density in question without any subtractions. Employment of the Hertz potentials for constructing the general solution to the Maxwell equations results in a considerable simplification of the calculations. Transition to the global zeta function is carried out by introducing a cutoff nearby the cusp …
Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multi…
Casimir entropy is an important aspect of casimir effect.In this paper,we employ the path integral method to derive the total relation for casimir entropy and internal energy of arbitrary shaped objects in the presence of two,three and four dimensions scalar fields and electromagnetic field.We obtain the casimir entropy and internal energy of two nanoribbon immersed in scalar field and two nanospheres immersed in scalar field and electromagnetic field.The casmir entropy of two nanospheres immersed in the electromagnetic field in small interval of temperature variations,shown a different behavi…
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 the general formalism in a number of cases which can be solved explicitly by analytical means. More in detail we deal with configurations involving parallel or perpendicular planes and we also discuss the case of a three-dimensional wedge.
One of J. Stuart Dowker's most significant achievements has been to observe that the theory of diffraction by wedges developed a century ago by Sommerfeld and others provided the key to solving two problems of great interest in general-relativistic quantum field theory during the last quarter of the twentieth century: the vacuum energy associated with an infinitely thin, straight cosmic string, and (after an interchange of time with a space coordinate) the apparent vacuum energy of empty space as viewed by an accelerating observer. In a sense the string problem is more elementary than the wedg…
We construct candidates for observables in wedge-shaped regions for a class of 1+1-dimensional integrable quantum field theories with bound states whose S-matrix is diagonal, by extending our previous methods for scalar S-matrices. Examples include the Z(N)-Ising models, the A_N-affine Toda field theories and some S-matrices with CDD factors. We show that these candidate operators which are associated with elementary particles commute weakly on a dense domain. For the models with two species of particles, we can take a larger domain of weak commutativity and give an argument for the Reeh-Schli…
Recently, large families of two-dimensional quantum field theories with factorizing S-matrices have been constructed by the operator-algebraic methods, by first showing the existence of observables localized in wedge-shaped regions. However, these constructions have been limited to the class of S-matrices whose components are analytic in rapidity in the physical strip. In this work, we construct candidates for observables in wedges for scalar factorizing S-matrices with poles in the physical strip and show that they weakly commute on a certain domain. We discuss some technical issues concernin…
In the bootstrap approach to integrable quantum field theories in the (1+1)-dimensional Minkowski space, one conjectures the two-particle S-matrix and tries to study local observables. The massless sine-Gordon model is conjectured to be equivalent to the Thirring model, and its breather-breather S-matrix components (where the first breather corresponds to the scalar field of the sine-Gordon model) are closed under fusion. Yet, the residues of the poles in this breather-breather S-matrix have wrong signs and cannot be considered as a separate model. We find CDD factors which adjust the signs, s…
We consider the quantum state seen by an observer in the diamond-shaped region, which is a globally hyperbolic open submanifold of the Minkowski space-time. It is known from the operator-algebraic argument that the vacuum state of the quantum field transforming covariantly under the conformal group looks like a thermal state on the von Neumann algebra generated by the field operators on the diamond-shaped region of the Minkowski space-time. Here, we find, in the case of the free massless Hermitian scalar field in the 2-dimensional Minkowski space-time, that such a state can in fact be identifi…
Recently, we have demonstrated that for a certain class of Casimir-type systems ("devices") the energy of zero-point vacuum fluctuations reaches its global minimum when the device rotates about a certain axis rather than remains static. This rotational vacuum effect may lead to the emergence of permanently rotating objects provided the negative rotational energy of zero-point fluctuations cancels the positive rotational energy of the device itself. In this paper, we show that for massless electrically charged particles the rotational vacuum effect should be drastically (astronomically) enhance…
The expectation values of energy density and pressure of a quantum field inside a wedge-shaped region appear to violate the expected relationship between torque and total energy as a function of angle. In particular, this is true of the well-known Deutsch--Candelas stress tensor for the electromagnetic field, whose definition requires no regularization except possibly at the vertex. Unlike a similar anomaly in the pressure exerted by a reflecting boundary against a perpendicular wall, this problem cannot be dismissed as an artifact of an ad hoc regularization.
