Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

The Unruh thermal spectrum through scalar and fermion tunneling

The thermal spectrum seen by accelerated observers in Minkowski space vacuum, the Unruh effect, is derived within the tunneling mechanism. This is a new result in this mechanism and it completes the treatment of Unruh effect via tunneling. Both Bose–Einstein and Fermi–Dirac spectrum is derived by considering tunneling of scalar and spin half particles respectively, across the accelerated Rindler horizon. Full solutions of massless Klein–Gordon and Dirac equations in the Rindler metric are employed to achieve this, instead of approximate solutions.     

Hyperfunction solutions of the zero-rest-mass field equations

In this paper it is shown how the Penrose transform maps tangential hyperfunction Dolbeault groups with coefficients in a power of the hyperplane section bundle on the hyperquadric of null twistors in projective twistor space isomorphically to all hyperfunction solutions of the massless field equations of nonnegative helicity on compactified Minkowski space. This is an extension of the Penrose transform which generated real-analytic solutions of the same field equations on the same space (cf. Eastwood, M., Penrose, R., Wells, R.O., [10]). In additions, one obtains the result that each hyperfunction solution of the massless field equations of nonnegative helicity is the sum of massless fields of positive and negative frequency, a generalization of the usual Fourier decomposition for solutions with appropriate growth conditions.     

Vacuum quantum effect for curved boundaries in static Robertson–Walker space–time

The energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in k=−1 static Robertson–Walker space–time is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the boundaries. k=−1 Robertson–Walker space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy–momentum tensor for conformally invariant field in Robertson–Walker space from the corresponding Rindler counterpart by the conformal transformation.     

CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge

Using Poincaré parametrization of AdS space, we study totally symmetric arbitrary spin massless fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized similarly to the ones of Stueckelberg formulation of massive fields. We demonstrate that the curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS fields can be expressed in terms of ladder operators. Realization of the global AdS symmetries in the conformal algebra basis is obtained. Modified de Donder gauge leading to simple gauge fixed Lagrangian is found. The modified de Donder gauge leads to decoupled equations of motion which can easily be solved in terms of the Bessel function. Interrelations between our approach to the massless AdS fields and the Stueckelberg approach to massive fields in flat space are discussed.     

The Maxwell and Proca equations in spaces with torsion

Nonlinear equations are derived for mass as well as massless vector fields in a Riemann space, where nonlinearity is induced by the interaction of these fields with individual irreducible parts of the torsion tensor. It is shown that in the simplest cases these equations are exactly solvable for an electromagnetic field, while a mass field is described by a number of interesting equations, in particular the sinh-Gordon equation, which has soliton solutions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 28–32, January, 1982.     

Supersymmetry and classical solutions

We obtain classical solutions to the field equations of the massless supersymmetric Wess-Zumino model and to the field equations of the interacting SU(2) gauge supermultiplet. This is done by applying finite supersymmetry transformations to the known solutions of the scalar field equation with ?⁴ interaction and the Yang-Mills field equations. The relevance of supersymmetry to the solution of classical field equations involving anticommuting fermion fields is discussed.     

Relativistic n-body wave equations in scalar quantum field theory

The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schrödinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.     

A plane symmetric solution of Einstein's field equations of general relativity containing zero-rest-mass scalar fields

An exact static solution of Einstein's field equations of general relativity in the presence of zero-rest-mass scalar fields has been obtained when both the metric tensor gijand the zero-rest-mass scalar field φexhibit plane symmetry in the sense of Taub [9]. Our solution generalizes the empty space-time solution with plane symmetry previously obtained by Taub to the situation when static zero-rest-mass scalar fields are present. The static plane symmetric solutoins of Einstein's field equations in the presence of massive scalar fields, and the difference between the massless and non-massless scalar fields are being investigated, and will be published separately later on. We also hope to discuss non-static plane symmetric solutions of Einstein's field equations in the presence of scalar fields in future.     

Properties of exact solutions for a massive classical Yang-Mills field

Exact solutions for a massive Yang-Mills field are found and solutions of classical Wong equations and quantum Dirac equations are discussed for the field configurations obtained. A procedure for constructing constant fields is given and transition to solutions of the Yang-Mills equations in the case of a massless field is discussed.Translated from Izvestriya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 96–100, May, 1986.In conclusion, the authors express their gratitude to V. Ch. Zhukovskii and V. R. Khalilov for valuable remarks and discussions.     

Rindler solutions and their physical interpretation

We show that the singular behavior of Rindler solutions near horizon testifies to the currents of particles from a region arbitrarily close to the horizon. Besides, the Rindler solutions in right Rindler sector of Minkowski space can be represented as a superposition of only positive-or only negative-frequency plane waves; these states require infinite energy for their creation and possess infinite charge in a finite space interval, containing the horizon. The positive-or negative-frequency representations of Rindler solutions analytically continued to the whole Minkowski space make up a complete set of states in this space, which have, however, the aforementioned singularities. These positive (negative)-frequency states are characterized by positive (negative) total charge, the charge of the same sign in right (left) Rindler sector and by quantum number κ. But in other Lorentz invariant sectors they do not possess positive (negative)-definite charge density and have negative (positive) charge in left (right) Rindler sector. Therefore these states describe both the particle (antiparticle) and pairs, the mean number of which is given by Planck function of κ. These peculiarities make the Rindler set of solutions nonequivalent to the plane wave set and the inference on the existence of thermal currents for a Rindler observer moving in empty Minkowski space is unfounded. Zh. éksp. Teor. Fiz. 114, 777–785 (September 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Hertz Potentials and Asymptotic Properties of Massless Fields

In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces. We prove existence and pointwise estimates for the Hertz potentials using a weighted estimate for the wave equation. This is then applied to give weighted estimates for the solutions of the spin-s field equations, for arbitrary half-integer s. In particular, the peeling properties of the free massless spin-s fields are analyzed for initial data in weighted Sobolev spaces with arbitrary, non-integer weights.     

Massless Fields on Dirac Six-Cone and De Sitter Ambient Space

We have proceeded to obtain manifestly conformally invariant (CI) equations for thinkable graviton fields in de Sitter (dS) space-time. The tensor fields are originally considered in 4+2 dimensional conformal space or Dirac’s six-cone and then project to dS space which is embedded in 4+1 dimensional ambient space. It will be shown that, by projecting these tensor fields there exists a correspondence between the massless fields on the cone and dS space. Also, we have shown that for rank-2 tensor field the divergenceless condition, which is necessary when we attempt to correspond the tensor field with the unitary irreducible representations (UIRs) of dS group, is not really a condition at all, it is a consequence of ambient space property. Due to the combined occurrences of corresponding fields and divergenceless property, the appropriate CI field equations have obtained in a fairly simple way and without imposing any extra condition.     

A minimal relativistic model of gravitation within standard restrictions of the Classical Theory of Fields

The minimal relativistic model of gravitation on the basis of the gauge-invariant theory of the linear scalar massless field is suggested. The principle of the multiplicative inclusion of gravitational interaction, the requirements being that the simplicity and invariance of the theory under the allowed (gauge) transformation of potential Ф → Ф′ = Ф + const as the basis of the approach, is used. A system of gauge-invariant gravitational field and matter equations is obtained and an energy-momentum tensor with a positively defined density of the field energy is constructed. The exact solutions to equations for the central static field and for fields of spherically symmetric and plane gravitational waves in the free space and in the material media are obtained.     

Effective Action for Scalar Fields in Two-Dimensional Gravity

We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and a general solution of the equations of motion in the massless case is reviewed. In the presence of a scalar field all geometric fields (zweibein and Lorentz connection) are excluded from the model by solving exactly their Hamiltonian equations of motion. In this way the effective equations of motion and the corresponding effective action for a scalar field are obtained. It is written in a Minkowskian space-time and does not include any geometric variables. The effective action arises as a boundary term and is nontrivial both for open and closed universes. The reason is that unphysical degrees of freedom cannot be compactly supported because they must satisfy the constraint equation. As an example we consider spherically reduced gravity minimally coupled to a massless scalar field. The effective action is used to reproduce the Fisher and Roberts solutions.     

Cosmological aspects of the gravitational interaction of a scalar field in the affine-metric theory of gravitation

The gravitational interaction of a scalar field, with allowance for the possible influence of the torsional and nonmetric nature of space-time, is investigated within the framework of the affine-metric theory of gravitation. The equations of the theory are derived from the variational principle. It is shown that in an affine-metric space, the combined Lagrangian of the gravitational and scalar fields with conformal coupling is reduced to the Lagrangian of the system of gravitational and axion fields in the general theory of relativity. All of the exact general solutions of the consistent system of equations of gravitational and scalar (massless) fields in the affine-metric space under consideration are obtained for all types of homogeneous Friedmann cosmological models, with the initial singularity being removed from some of them. Homogeneous, anisotropic cosmological models, for which all of the exact general solutions are also obtained, are investigated. Some of these models are nonsingular, and the effect of isotropization due to the torsional and nonmetric nature of space-time occurs for many of them. K. D. Ushinskii State Pedagogical University, Yaroslavl’. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 39–50, May, 1998.     

Frame-like actions for massless mixed-symmetry fields in Minkowski space

A frame-like action for arbitrary mixed-symmetry bosonic massless fields in Minkowski space is constructed. The action is given in a simple form and consists of two terms for a field of any spin. The fields and gauge parameters are certain tensor-valued differential forms. The formulation is based on the unfolded form of equations for mixed-symmetry fields.     

Analysis of the wave functions for accelerating Kerr-Newman metric

As is well-known, it is very difficult to solve wave equations in curved space-time. In this paper,we find that wave equations describing massless fields of the spins s≤2 in accelerating KerrNewman black holes can be written as a compact master equation. The master equation can be separated to radial and angular equations, and both can be transformed to Heun's equation,which shows that there are analytic solutions for all the wave equations of massless spin fields.The results not only demonstrate that it is possible to study the similarity between waves of gravitational and other massless spin fields, but also it can deal with other astrophysical applications, such as quasinormal modes, scattering, stability, etc. In addition, we also derive approximate solutions of the radial equation.     

Tensor Lagrangians,Lagrangians Equivalent to the Hamilton-Jacobi Equation and Relativistic Dynamics

We deal with Lagrangians which are not the standard scalar ones. We present a short review of tensor Lagrangians, which generate massless free fields and the Dirac field, as well as vector and pseudovector Lagrangians for the electric and magnetic fields of Maxwell’s equations with sources. We introduce and analyse Lagrangians which are equivalent to the Hamilton-Jacobi equation and recast them to relativistic equations.     

On the free scalar massless field in two-dimensional space-time

In the present paper the solutions of the quantum field problem for the free scalar massless field in two-dimensional space time are constructed. It is shown that the fields obtained cannot vanish at space-like infinity. The latter fact implies the existence of two conserved charge operators. The transformation properties of these solutions under the two-dimensional Lorentz group are examined.