The energy—momentum tensor, the trace identity and the Casimir effect

The trace identity associated with the scale transformation x^Μ → x′^Μ = e^-ρx^Μ on the Lagrangian density for the noninteracting electromagnetic field in the co-variant gauge is shown to be violated on a single plate on which the Dirichlet boundary conditionA ^Μ(t, x¹, x², x³ = -a) = 0 is imposed. It is however respected in free space, i.e. in the absence of the plate. These results reinforce our assertions in an earlier paper where the same exercise was carried out using the Lagrangian density for the free, massive, real scalar field in 2 + 1 dimensions.     

The Casimir effect of Reissner-NordstrSm black hole

The stress tensor of a massless scalar field satisfying a mixed boundary condition in a （1 ＋ 1）-dimensional Reissner- Nordstrom black hole background is calculated by using Wald＇s axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.     

The Casimir interaction of a massive vector field between concentric spherical bodies

The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, there are no TM discrete modes that vanish identically in the perfectly conducting spherical bodies. Numerical simulations show that the Casimir interaction force between the two bodies is always attractive.     

Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions

We consider the finite temperature Casimir effect of a massive fermionic field confined between two parallel plates, with MIT bag boundary conditions on the plates. The background spacetime is Mp+1×Tq which has q dimensions compactified to a torus. On the compact dimensions, the field is assumed to satisfy periodicity boundary conditions with arbitrary phases. Both the high temperature and the low temperature expansions of the Casimir free energy and the force are derived explicitly. It is found that the Casimir force acting on the plates is always attractive at any temperature regardless of the boundary conditions assumed on the compact torus. The asymptotic limits of the Casimir force in the small plate separation limit are also obtained.     

Casimir效应的一个简明计算

电磁场的真空态具有无穷大的能量,这个无穷大能量不可直接观测,只在某些特殊情况下才表现出可观测的效应,其中之一便是Casimir效应,通常这个效应的计算是在量子场论中,按重正化的办法进行,这里给出一个更为简明的算法。     

Casimir Effect of Massive Scalar Field with Hybrid Boundary Condition in （1＋1）-Dimensional Spacetime

The Casimir energy of massive scalar field with hybrid （Diriehlet-Neumann） boundary condition is calculated. In order to regularize the model, the typical methods named as mode summation method and Green＇s function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field＇s mass. When the field is massless, the result is consistent with previous literatures.     

The Casimir effect and the fine structure constant

We consider the electron as a charged sphere that completely absorbs any radiation with wave number less than somek _m . The Casimir effect then provides a self stress which can balance the mutual repulsion of the distinct parts of the finite charge distribution. From this equilibrium condition and connecting, by quantum arguments, the value ofk _m to the radius of the electron, we obtain a good estimate for the value of the fine-structure constant.     

Quantum spring from the Casimir effect

The Casimir effect arises not only in the presence of material boundaries but also in space with nontrivial topology. In this Letter, we choose a topology of the flat (D+1)$(D+1)$-dimensional spacetime, which causes the helix boundary condition for a Hermitian massless scalar field. Especially, Casimir effect for a massless scalar field on the helix boundary condition is investigated in two and three dimensions by using the zeta function techniques. The Casimir force parallel to the axis of the helix behaves very much like the force on a spring that obeys the Hooke's law when the ratio r of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so we would like to call it quantum spring. When r is large, this force behaves like the Newton's law of universal gravitation in the leading order. On the other hand, the force perpendicular to the axis decreases monotonously with the increasing of the ratio r. Both forces are attractive and their behaviors are the same in two and three dimensions.     

The Casimir effect for fields with arbitrary spin

The Casimir force arises when a quantum field is confined between objects that apply boundary conditions to it. In a recent paper we used the two-spinor calculus to derive boundary conditions applicable to fields with arbitrary spin in the presence of perfectly reflecting surfaces. Here we use these general boundary conditions to investigate the Casimir force between two parallel perfectly reflecting plates for fields up to spin-2. We use the two-spinor calculus formalism to present a unified calculation of well-known results for spin-1/2 (Dirac) and spin-1 (Maxwell) fields. We then use our unified framework to derive new results for the spin-3/2 and spin-2 fields, which turn out to be the same as those for spin-1/2 and spin-1. This is part of a broader conclusion that there are only two different Casimir forces for perfectly reflecting plates—one associated with fermions and the other with bosons.     

Neumann Casimir effect: A singular boundary-interaction approach

Dirichlet boundary conditions on a surface can be imposed on a scalar field, by coupling it quadratically to a δ-like potential, the strength of which tends to infinity. Neumann conditions, on the other hand, require the introduction of an even more singular term, which renders the reflection and transmission coefficients ill-defined because of UV divergences. We present a possible procedure to tame those divergences, by introducing a minimum length scale, related to the nonzero ‘width’ of a nonlocal term. We then use this setup to reach (either exact or imperfect) Neumann conditions, by taking the appropriate limits. After defining meaningful reflection coefficients, we calculate the Casimir energies for flat parallel mirrors, presenting also the extension of the procedure to the case of arbitrary surfaces. Finally, we discuss briefly how to generalize the worldline approach to the nonlocal case, what is potentially useful in order to compute Casimir energies in theories containing nonlocal potentials; in particular, those which we use to reproduce Neumann boundary conditions.     

卡西米尔效应的格林函数计算方法

介绍了卡西米尔效应的严格格林函数表达式.作为应用,计算了4种边界条件下两平行板之间的卡西米尔能量.     

Casimir Effect for Dielectric Plates

We generalize Kupisewska method to the three-dimensional system and another derivation of the Casimir effect between two dielectric plates is presented based on the explicit quantization of the electromagnetic field in the presence of dielectrics, where the physical meaning of “evanescent mode” is discussed. The Lifshitz's formula is rederived using all the vacuum mode functions, which include the contribution of the ‘evanescent modes’. Only in the case of the perfect metallic plates will the evanescent modes become unimportant.     

The extended trace identity and its application

The trace identity is extended to the general loop algebra. The Hamiltonian structures of the integrable systems concerning vector spectral problems and the multi-component integrable hierarchy can be worked out by using the extended trace identity. As its application, we have obtained the Hamiltonian structures of the Yang hierarchy, the Korteweg-de--Vries (KdV) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur Kaup--Newell (M-AKNS--KN) hierarchy and a new multi-component integrable hierarchy separately.     

The Casimir pressure regularization in two-dimensional field models

A method for Casimir pressure calculation with the help of the regular part of the Green surface function is considered in the two-dimensional case. Also, a method for the approximate calculation of the regular part of the Green surface function using a Born-type series is suggested. It is tested for a problem for which the exact solution is known.     

Number of particle creation and decoherence in the nonideal dynamical Casimir effect at finite temperature

In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary, under the only restriction of small velocities. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of a slow moving boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boundary. On the basis of these expressions we develop a comprehensive analysis of the resonances in the number of particle creation in the nonideal dynamical Casimir effect. We also demonstrate the occurrence of resonances in the loss of purity of the initial state and estimate the decoherence times associated with these resonances. Since our results were obtained in the framework of the perturbation theory, they are restricted, under resonant conditions, to a short-time approximation.     

Cosmological Particle Creation and Dynamical Casimir Effect

We compute particle creation for a real massive scalar field conformally coupled to a spatially closed Robertson–Walker space-time background, with time-dependent scale factor. This is a dynamical Casimir effect with moving boundaries.     

The correspondence between Casimir pressure and energy in one-dimensional field models

We propose a method of calculation of Casimir pressure using the Green function for one-dimensional case. This method yields the renormalized pressure if an external field is absent, otherwise it permits us to calculate the dependence of pressure at one boundary on the other boundary’s coordinate. The calculated pressure permits one to obtain the Casimir energy for the systems under consideration.     

Radiative Corrections to Casimir Force of Maxwell-Chern-Simons Gauge Field

We discuss the two-loop radiative correction to the Casimir force ofMaxwell-Chern-Simons Abelian gaugefield between two parallel ideal conducting wires in terms of Feynman path integral method.     

Dynamical Casimir effect in uniformly accelerated media

Photon production by an oscillating medium predicted in [I. Bialynicki-Birula, Z. Bialynicka-Birula, Phys. Rev. A 78 (2008) 042109] is analyzed for a uniformly accelerated medium. The density of produced photons is found analytically in terms of Legendre functions. Under normal laboratory conditions the effect is extremely small.