Problems of classical and quantum-gravitational collapse V. (Quantum cosmology. scalar field. continuation)

The study of the system of homogeneous gravitational and scalar fields is continued in the framework o f the formalism of canonical quantization. Solution of de Witt's equation by perturbation theory leads to the prediction of production of scalar matter by a nonstationary quantized gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 115–118, August, 1977.We are very grateful to V. G. Krechet for stimulating discussions and also to V. R. Khalilov and D. V. Gal'tsov for valuable comments and discussion of the work.     

Problems of classical and quantum-gravitational collapse

The quantization of a homogeneous isotropic Friedmann model of the universe that is occupied by a quantized scalar field is considered in the superspace approach of Wheeler and DeWitt. Steady-state perturbation theory is used to show that in the region N 1, 10^–23, N=1, 2,..., where it is applicable, the steady-state solutions of the DeWitt equation have a discrete spectrum corresponding to discrete energy levels of the steady state of the cosmological model M= (2N + 1)M_o, M_o = 10^–5 g.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 113–117, July, 1977.In conclusion the authors thank Sen. Sci. Colleague D. V. Galtsov and Sen. Sci. Colleague V. R. Khalilov, and also the members of the seminar conducted by Profs. V. P. Shelest and K. P. Stanyukovich.     

Coupling of massless particles to scalar fields

It is investigated whether massless particles can couple to scalar fields in a special-relativistic theory with classical particles. The only possible obvious theory which is invariant under Lorentz transformationsand reparametrization of the affine parameter leads to trivial trajectories (straight lines) for the massless case, and also the investigation of the masslesslimit of the massive theory shows that there is no influence of the scalar field on the limiting trajectories. On the other hand, in contrast to this result, it is shown that massive particlesare influence by the scalar field in this theory even in the ultrarelativistic limit.     

Massive or massless scalar field and confinement

The generalization of QCD motivated classical SU(2) Yang-Mills theory coupled to a scalar field is discussed. The massive scalar field, corresponding to the scalar glueball, provides a confining potential for static, point-like, external sources. In the case of a massless scalar field screening solutions are found. However, there is a confining sector as well. Both, massive and massless confining solutions, are compared with phenomenological potentials. The case of a non-dynam ical permittivity is also discussed. Received: 15 November 2002 / Revised version: 31 January 2003 / Published online: 7 March 2003 RID="a" ID="a" e-mail: mslus@phys.ualberta.ca RID="b" ID="b" e-mail: wereszcz@alphas.if.uj.edu.pl     

Gravitational stability of a massless scalar field

A solution is obtained to the Einstein equations for a static, spherically symmetric, massless scalar field. The stability of a static, massless scalar field for a point source is studied. It is found that the field is unstable for small ratios of the scalar charge of the source to its mass but is stable for large ratios. It is proven that there exists a dimensionless number which limits the region of stability for the field.Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Fizika, No. 7, pp. 79–83.     

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.     

Classical limit of the Casimir entropy for scalar massless field

We study the Casimir effect at finite temperature for a massless scalar field in the parallel plates geometry in N spatial dimensions, under various combinations of Dirichlet and Neumann boundary conditions on the plates. We show that in all these cases the entropy, in the limit where energy equipartitioning applies, is a geometrical factor whose sign determines the sign of the Casimir force.     

Nonstatic solutions for the repulsive massless scalar field Einstein equation

Presented in this paper are exact nonstatic solutions for the coupled repulsive sourceless massless scalar field and the gravitational field. The solutions have the same form as the spatially conformally flat static metricds ² =e ^2ψ dt ² +e ^?2ψ(dx ² +dy ² +dz ²).     

General relativity,the massless scalar field,and the cosmological constant

For gravity coupled to a neutral, massless scalar field, Wyman suggested a method of solution in power series valid provided the scalar field depends only on time. In this work we generalize his approach to nonzero cosmological constant.     

Dilatons and the dynamical collapse of charged scalar field

We studied the influence of dilaton field on the dynamical collapse of a charged scalar one. Different values of the initial amplitude of dilaton field as well as the altered values of the dilatonic coupling constant were considered. We described structures of spacetimes and properties of black holes emerging from the collapse of electrically charged scalar field in dilaton gravity. Moreover, we provided a meaningful comparison of the collapse in question with the one in Einstein gravity, when dilaton field is absent and its coupling with the scalar field is equal to zero. The course and results of the dynamical collapse process seem to be very sensitive to the amplitude of dilaton field and to the value of the coupling constant in the underlying theory.     

The exponential of the two-dimensional massless scalar field as an infrared Jaffe field

The definition of the Wick exponential of the massless scalar field in two dimensions as an operator-valued distribution is discussed in the Krein space realization of the field. It is shown that the exponential Wick power series converges strongly on a suitably dense domain, provided that it is smeared with test functions which satisfy some growth conditions in configuration space. Such conditions are similar to the high energy bounds previously introduced by Jaffe for the definition of strictly localizable fields. In this case it is found that the Wick exponential is strictly localizable in momentum space.     

Fourier representation for the two-point function of the two-dimensional massless scalar field

The Fourier transform of the (indefinite metric) Wightman two-point function of a free massless scalar quantum field in two-dimensional spacetime has been inconsistently reported by various authors. We compute the correct one from the definition of the Fourier transform of tempered distributions.     

Resonant frequencies of massless scalar field in rotating black-brane spacetime

This paper investigates the resonant frequencies of the massless scalar field in the near extremal Kerr-like black-brane spacetime. It is shown that the different angular quantum number will present different resonant frequencies. It is also shown that the real part of the resonant frequencies increases as the compact dimensions parameter μi increases, but the magnitude of the imaginary part decreases as μi increases.     

Problems of classical and quantum gravitational collapse

An exact solution of Einstein's equations is obtained in the case of a spherically symmetric distribution of a perfect fluid with maximally hard equation of state. A sufficient condition of halting of the collapse of charged dust is obtained. The dynamics and statics of a vector massive configuration with massless source are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–12, September, 1977.We are very grateful to N. V. Pavlov and K. A. Bronnikov for valuable discussions and helpful comments.     

Inflation inR 2 cosmology with massless conformal scalar field and adiabatic regularization

A cosmology described by a Robertson-Walker metric with Lagrangian -g(@#@R+R ²) and a massless conformal scalar field as matter content is considered. It is shown that, when the adiabatic regularization is performed, there is, in the spatially flat case, an inflationary solution which is not stable in the future, at first perturbative order, if the condition >t _p ² /2160 (t _p Planck time) is fulfilled and stable in the opposite case.     

Modular structure of the local algebras associated with the free massless scalar field theory

The modular structure of the von Neumann algebra of local observables associated with a double cone in the vacuum representation of the free massless scalar field theory of any number of dimensions is described. The modular automorphism group is induced by the unitary implementation of a family of generalized fractional linear transformations on Minkowski space and is a subgroup of the conformal group. The modular conjugation operator is the anti-unitary implementation of a product of time reversal and relativistic ray inversion. The group generated by the modular conjugation operators for the local algebras associated with the family of double cone regions is the group of proper conformal transformations. A theorem is presented asserting the unitary equivalence of local algebras associated with lightcones, double cones, and wedge regions. For the double cone algebras, this provides an explicit realization of spacelike duality and establishes the known typeIII ₁ factor property. It is shown that the timelike duality property of the lightcone algebras does not hold for the double cone algebras. A different definition of the von Neumann algebras associated with a region is introduced which agrees with the standard one for a lightcone or a double cone region but which allows the timelike duality property for the double cone algebras. In the case of one spatial dimension, the standard local algebras associated with the double cone regions satisfy both spacelike and timelike duality.Supported by the National Science Foundation under Grant No. PHY-79-23251Supported in part by C. N. R.     

Exact solution of a massless scalar field with a relevant boundary interaction

We solve exactly the “boundary sine-Gordon” system of a massless scalar field with a potential at a boundary. This model has appeared in several contexts, including tunneling between quantum-Hall edge states and in dissipative quantum mechanics. For β² < 8π, this system exhibits a boundary renormalization-group flow from Neumann to Dirichlet boundary conditions. By taking the massless limit of the sine-Gordon model with boundary potential, we find the exact S-matrix for particles scattering off the boundary. Using the thermodynamic Bethe ansatz, we calculate the boundary entropy along the entire flow. We show how these particles correspond to wave packets in the classical Klein-Gordon equation, thus giving a more precise explanation of scattering in a massless theory.