Separation of the massless spin-1 equation in Robertson-Walker space-time

The massless spin-1 free field equation is studied via the Newman-Penrose formalism and separated by the Chandrasekhar-Teukolski method. The temporal and angular equations are explicitly integrated. The radial equations are solved in the flat-universe case. The closed-universe case shows, in principle, the existence of a discrete spectrum of the energy of the massless particles.     

Gauge theory of massless spin-(3/2) field in de Sitter space-time

On several levels of theoretical physics, especially particle physics and early universe cosmology, de Sitter space-time has become an attractive possibility. The principle of local gauge invariance governs all known fundamental interactions of elementary particles, from electromagnetism and weak interactions to strong interactions and gravity. This paper presents a procedure for defining the gauge-covariant derivative and gauge invariant Lagrangian density in de Sitter ambient space-time formalism. The gauge invariant field equation is then explicitly calculated in detail for a massless spin-(3/2) gauge field.     

Sine-Gordon equation in curved space-time

We study the static solution of the sine-Gordon wave equation in a background geometry determined by a point mass in 1+1 dimension.     

Dirac equation in (1+1)-dimensional curved space-time

The Dirac equation in (1+1)-dimensional curved space-time is solved explicitly for the spatially flat Robertson-Walker space-time and the cigar metric considered by Witten.     

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.     

Renormalization group equation for the vacuum energy of a scalar field in curved space-time

The renormalization group equation is formulated for the vacuum energy of a scalar field. We calculate the two-loop functions and study the asymptotic behavior of the vacuum energy.     

Proca fields interpretation of spin 1 equation in Robertson-Walker space-time

The general scheme for massive spin 1 equation in curved space-time is specialized to describe the Proca fields. The expressions of the Proca tensor fields are detailed in the Robertson-Walker space-time by means of the solutions of the spin 1 equation in a given tetrad and by the components of the tetrad itself. Asymptotic behaviours of the fields are discussed in the flat, closed and open space-time cases.Also GNFM, Italy     

Free massless scalar field in two-dimensional space-time: Revisited

The indefinite-metric quantum field theory of the two-dimensional free massless scalar field proposed previously is reinvestigated. In order to reply to various criticisms of it, subtle points are discused in detail, and it is shown that the formalism is free from contradictions. In particular, its is emphasized that the non-uniqueness of the translationally invariant states is consistent with the irreducibility of the field algebra in the theory with indefinite metric.     

Optical theorem in curved space-time quantum field theory

A structural analysis is given of the optical theorem in theS-matrix approach to mutually interacting quantum fields in classical Robertson-Walker universes. As a case study, theφψ ²-interaction of conformally coupled massive (φ) and massless (φ) Klein-Gordon particles is studied. Based on the outgoing massless particles as indicator configuration, the physical interpretation is reduced to the corresponding added-up probabilities. Several examples are discussed in an in-in scheme which has the advantage that only a few non-Minkowskian in-in Feynman diagrams are involved.     

On free massless (pseudo)scalar quantum field theory in 1+1-dimensional space-time

We construct a consistent quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-times free of infrared divergences. We show that in such a quantum field theory (i) a continuous symmetry of (pseudo)scalar field translations is spontaneously broken, (ii) Goldstone bosons appear as quanta of a free massless (pseudo)scalar field and (iii) there is a non-vanishing spontaneous {magnetization}. In spite of the existence of a spontaneous {magnetization} the main inequality between vacuum expectation values of certain operators which have been used for the derivation of the Mermin–Wagner–Hohenberg theorem (C. Itzykson and J.-M. Drouffe, {Statistical field theory}, Vol. I, 1989, pp. 219–224) is fulfilled. Received: 19 December 2001 / Revised version: 31 March 2002 / Published online: 14 June 2002     

Scalar field equation in Robertson-Walker space-time

The quantization of the scalar field is reconsidered in some of its basic elements in the context of the Robertson-Walker space-time. The integration of the generalized Klein-Gordon equation is performed by preliminary separation of the equation with the usual separation method. The orthonormal mode solutions are determined by the explicit integration of the resulting angular and radial equations and by standard properties of the time equation. The time evolution given by the standard cosmological model is briefly discussed.     

On the bound states of the massless free field in two space-time dimensions

We point out the peculiar kinematics of zero-mass fields in two space-time dimensions by showing that the n-fold tensor product of one-particle representations of the Poincaré group for n ? 2 contains a countable infinity of discrete, zero-mass representations. We relate this result to the well-known “bound” states in every charge sector of the fermion Fock space.     

Quantum field theory in curved space-time as thermo field dynamics

The strong analogy between states defined in the context of quantum field theory in curved space-time (QFT-CST) and the ones defined in the thermo field dynamics (TFD) of Takahashi and Umezawa [1] is shown. This analogy is useful in order to introduce the entropy operator in CST in the same way as in TFD. When the extremum condition in the thermodynamical potential is imposed, a family of Bogoliubov transformations that give us a planckian spectrum is found, even in pathological cases such as the minimally coupled scalar field.     

The problem of scalar field theory in curved space-time

It is demonstrated that (1) there exist infiniteG ₁ that satisfy Lichnerowicz's conditions (L conditions) in a globally hyperbolic manifold; and, (2) there is noG ₁ in an expanding universe that would satisfy those conditions and that would behave as the ordinary ₁ of flat space whenx x. The author thinks that these results present a serious problem for finding a semiclassical theory of scalar field in curved space-time.     

Electromagnetic field in two-dimensional locally flat space-time

It is shown that an infinite-dimensional symmetry is present in two-dimensional electromagnetic field theory. The generators of the ensuing Virasoro algebra are explicitly calculated both for periodic and antiperiodic fields.     

Renormalization of interacting scalar field theories in curved space-time

The renormalization structure of the quantum theory of a scalar field with the interaction ⁴ is investigated in curved space-time. The form of the renormalized action and its dependence on the nonminimal coupling are found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 57–62, December, 1984.The author is grateful to B. L. Voronov, I. V. Tyutin, and E. S. Fradkin for discussions concerning this work.     

Dimensional renormalization of scalar field theory in curved space-time

The regularization and renormalization of an interacting scalar field φ in a curved spacetime background is performed by the method of continuation to n dimensions. In addition to the familiar counter terms of the flat-space theory, c-number, “vacuum” counter terms must also be introduced. These involve zero, first, and second powers of the Reimann curvature tensor R_αβψδ. Moreover, the renormalizability of the theory requires that the Lagrange function couple φ² to the curvature scalar R with a coupling constant η. The coupling η must obey an inhomogeneous renormalization group equation, but otherwise it is an arbitrary, free parameter. All the counter terms obey renormalization group equations which determine the complete structure of these quantities in terms of the residues of their simple poles in n ? 4. The coefficient functions of the counter terms determine the construction of φ² and φ⁴ in terms of renormalized composite operators 1, [φ²], and [φ⁴]. Two of the counter terms vanish in conformally flat space-time. The others may be computed from the theory in purely flat space-time. They are determined, in a rather intricate fashion, by the additive renormalizations for two-point functions of [φ²] and [φ⁴] in Minkowski space-time. In particular, using this method, we compute the leading divergence of the R² interaction which is of fifth order in the coupling constant λ.     

Existence of the S-matrix in quantum field theory in curved space-time

The existence of the S-matrix is proven for particle creation by an external gravitational field of compact support. No infrared divergences occur even for massless quantum fields; in particular, a localized gravitational field always produces a finite expected total number of particles. The results of this paper apply to both boson and fermion fields as well as to more general linear, external potential interactions.     

A classification of massless totally antisymmetric tensor field in arbitrary dimensional space-time

A formulation of the massless fields is given in terms of a system of first-order equations. There are two such systems, and the massless fields are accordingly classified into two families. Successive gauge transformations exist, by which the sequential FP ghosts are induced. The number of physical modes is counted easily by looking at the field strength.