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.     

Vacuum Effects on Massive Spinor Fields: S 1× R 3 Topology

The aim of this work was to investigate the role played by an external field on the Casimir energy density for massive fermions under S ¹× R ³ topology. Both twisted- and untwisted-spin connections are considered and the calculation in a closed form is performed using an alternative approach based on the combination of the analytic regularization method and the Euler–Maclaurin summation formula. It is shown that no mass scale appears in the final result and, therefore, Casimir effect arises only from the boundary conditions and vacuum fluctuations induced by the coupling with the external field. PACS numbers: 11.10.Wx     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both flat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimir effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet ard Neumann boundary conditions are also discussed.     

On the Casimir effect without cutoff

The formulation of the Casimir effect without cutoffs is discussed. Our derivation emphasizes the decisive role of the free-space electromagnetic energy density. The zero point energy arises as an energy per unit volume, i.e., as local (in x space) energy density. It is given by the vaccum expectation value of the free-space Hamiltonian density in the Fock representation corresponding to the non-trivial geometry. The two Fock representations corresponding to the system with and without plates are proved to be inequivalent.     

Attractive and repulsive Casimir vacuum energy with general boundary conditions

The infrared behaviour of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth–Klich theorem and that the strongest attractive Casimir force appears for periodic boundary conditions whereas the strongest repulsive Casimir force corresponds to anti-periodic boundary conditions. Most of the analysed boundary conditions are new and some of them can be physically implemented with metamaterials.     

Casimir pressure renormalization by the method of efficient surface charges

The problem of regularization and renormalization of the Casimir pressure in a finite area with a smooth boundary is considered using the example of a real scalar field in the two-dimensional case. A procedure for the renormalization of boundary pressure using a certain modified area and a method for approximate calculation of the Green’s function and its derivatives with the use of efficient surface charges are proposed. For problems that allow an exact solution, it is shown that the method has high accuracy and computational efficiency.     

Thermodynamics of the Casimir effect

A complete thermodynamic treatment of the Casimir effect is presented. Explicit expressions for the free and the internal energy, the entropy and the pressure are discussed. As an example we consider the Casimir effect with different temperatures between the plates (T) resp. outside of them (T'). For T'<T the pressure of heat radiation can eventually compensate the Casimir force and the total pressure can vanish. We consider both an isothermal and an adiabatic treatment of the interior region. The equilibrium point (vanishing pressure) turns out instable in the isothermal case. In the adiabatic situation we have both an instable and a stable equilibrium point, if T'/T is sufficiently small. Quantitative aspects are briefly discussed. Received 24 February 1999 and Received in final form 26 April 1999     

State sum invariants of three-manifolds: A combinatorial approach to topological quantum field theories

The construction of Turaev and Viro involving quantum 6j-symbols and giving rise to invariants of closed, compact three-manifolds is extended. It leads to invariants of coloured graphs on the boundary of compact three-manifolds. This allows one to derive surgery formulas when cutting along an arbitrary two-manifold. In particular all axioms of a topological quantum field theory may be verified and the dimensions of the associated Hilbert spaces are given by the square of the Verlinde formula.     

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 Effect Under Two Dimensional Black Hole Spacetime Background with Global Monopole

A thin layer of the event horizon vicinity to the two-dimension black hole with a global monopole is considered as a system of the Casimir type. The energy-momentum tensor is derived in Boulware vacuum, Hartle-Hawking vacuum and Unruh vacuum respectively. The values are derived in the massless scalar field which satisfies the Dirichlet boundary conditions. Using the Wald's axioms, the result is got which is the same with the one derived by the usual regularized methods. Meanwhile, the energy, energy density, and pressure acting on the boundaries at the asymptotically flat background also are calculated too, and from the energy, Casimir force is derived. The Casimir energy and Casimir force are compared respectively in the background before and after radiation. PACS: 42.50.Lc.     

The Casimir Problem of Spherical Dielectrics: A Solution in Terms of Quantum Statistical Mechanics

The Casimir energy for a compact dielectric sphere is considered in a novel way, using the quantum statistical method introduced by Høye and Stell and others. Dilute media are assumed. It turns out that this method is a very powerful one: we are actually able to derive an expression for the Casimir energy that contains also the negative part resulting from the attractive van der Waals forces between the molecules. It is precisely this part of the Casimir energy that has turned out to be so difficult to extract from the formalism when using the conventional field-theoretic methods for a continuous medium. Assuming a frequency cutoff, our results are in agreement with those recently obtained by G. Barton.     

柱环腔中的量子电动力学效应

研究以同轴不同半径柱面围成的导体柱环腔体中电磁场真空零点振动模式所给出的宏观量子效应.零点振动模式通过求解柱环空腔边界条件下无源的Maxwell方程组获得.得到了双柱面同心柱环中单位长度和单位面积的且是有限的真空能量，即Casimir能量.这有限的Casimir能量可以分解为独立而且收敛的三部分，它们分别来自内柱面、外柱面和柱环之中.对多柱面同心柱环，Casimir能量可分解为独立的（2n—1）部分（n为柱面数）.柱环是类似于平行板的几何结构.但柱环所给出的Casimir能量和Casimir势能系数是随着 关键词： Casimir效应 柱环腔体 零点能 量子电动力学     

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension δ is within its allowed region. We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.     

Essay: Quantum Field Theory Is Not Merely Quantum Mechanics Applied to Low Energy Effective Degrees of Freedom

It is commonly assumed that quantum field theory arises by applying ordinary quantum mechanics to the low energy effective degrees of freedom of a more fundamental theory defined at ultra-high-energy/short-wavelength scales. We shall argue here that, even for free quantum fields, there are holistic aspects of quantum field theory that cannot be properly understood in this manner. Specifically, the subtractions needed to define nonlinear polynomial functions of a free quantum field in curved spacetime are quite simple and natural from the quantum field theoretic point of view, but are at best extremely ad hoc and unnatural if viewed as independent renormalizations of individual modes of the field. We illustrate this point by contrasting the analysis of the Casimir effect, the renormalization of the stress-energy tensor in time-dependent spacetimes, and anomalies from the point of quantum field theory and from the point of view of quantum mechanics applied to the independent low energy modes of the field. Some implications for the cosmological constant problem are discussed.     

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 for fermions in one dimension

We study the Casimir problem for a fermion coupled to a static background field in one space dimension. We examine the relationship between interactions and boundary conditions for the Dirac field. In the limit that the background becomes concentrated at a point (a “Dirac spike”) and couples strongly, it implements a confining boundary condition. We compute the Casimir energy for a masslike background and show that it is finite for a stepwise continuous background field. However the total Casimir energy diverges for the Dirac spike. The divergence cannot be removed by standard renormalization methods. We compute the Casimir energy density of configurations where the background field consists of one or two sharp spikes and show that the energy density is finite except at the spikes. Finally we define and compute an interaction energy density and the force between two Dirac spikes as a function of the strength and separation of the spikes.     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both fiat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimlr effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet and Neumann boundary conditions are also discussed.     

The Casimir Effect for Parallel Plates in the Spacetime with a Fractal Extra Compactified Dimension

The Casimir effect for massless scalar fields satisfying Dirichlet boundary conditions on the parallel plates in the presence of one fractal extra compactified dimension is analyzed. We obtain the Casimir energy density by means of the regularization of multiple zeta function with one arbitrary exponent. We find a limit on the scale dimension like $\delta>\frac{1}{2}$ to keep the negative sign of the renormalized Casimir energy which is the difference between the regularized energy for two parallel plates and the one with no plates. We derive and calculate the Casimir force relating to the influence from the fractal additional compactified dimension between the parallel plates. The larger scale dimension leads to the greater revision on the original Casimir force. The two kinds of curves of Casimir force in the case of integer-numbered extra compactified dimension or fractal one are not superposition, which means that the Casimir force show whether the dimensionality of additional compactified space is integer or fraction.     

Lattice quantum chromodynamics equation of state: A better differential method

We propose a better differential method for the computation of the equation of state of QCD from lattice simulations. In contrast to the earlier differential method, our technique yields positive pressure for all temperatures including the temperatures in the transition region. Employing it on temporal lattices of 8, 10 and 12 sites and by extrapolating to zero lattice spacing we obtained the pressure, energy density, entropy density, specific heat and speed of sound in quenched QCD for 0.9 ≤ T/T _c ≤ 3. At high temperatures comparisons of our results are made with those from the dimensional reduction approach and also with those from a conformal symmetric theory.