Gravitational and quantum effects in rotating cosmological models

Specific effects of the dynamics of (spinor and scalar) wave fields are considered in rotating uniform Gödel-type cosmological models. It is shown that the gravitational interaction of the spinor field can be reduced to the interaction between its pseudovector current and the angular velocity of space-time rotation and is similar to its interaction with the pseudotrace of the space-time twisting. The mean values of energy-momentum tensor of the quantized scalar field in vacuum are calculated in rotating cosmological models and the difference between these values and their mean counterparts in vacuum is determined for Friedman's nonrotating cosmological models.State Education Institute, Yaroslavl'. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 35–38, June, 1992.     

Definition of the vacuum in curved space-time

It is proposed that the vacuum state of quantized fields in curved space-time be defined as the state which minimizes the average value of the field Hamiltonian. Starting from this definition, equations are obtained for finding positive- and negative-frequency functions for spinor and scalar fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 16–21, July, 1979.     

Quantum effects in cosmological models with singularities

The vacuum expectation values of the energy-momentum tensor of quantized scalar and spinor fields in a de Sitter space of the first kind are calculated. Limiting cases of the obtained exact expressions are considered. It is noted that the de Sitter space is a self-consistent solution of the Einstein equations with allowance for quantum vacuum fluctuations of massless fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 67–70, January, 1981.I thank V. M. Mostepanenko and B. N. Sharapov for numerous helpful discussions.     

Vacuum charge and the eta function

The vacuum charge of a second quantized spinor field in a static classical background field on a static spacetime is studied. Wheng ₀₀=1 the vacuum charge is shown to be essentially the eta function of the spinor Hamiltonian ats=0. This is computed for compact and noncompact spaces and a boundary dependence is derived in the latter case.     

A Quantum Cosmological Bianchi I Model with Interacting Spinor and Scalar Fields

A Bianchi I model of the Universe filled with interacting nonlinear spinor and scalar fields is studied within quantum geometrodynamics. Three types of interaction are considered: gradient, Yukawa, and axion ones. For massless fermion fields, the variables in the Wheeler – de Witt equation will separate. The solution can be interpreted using a two-component perfect liquid. One component corresponds to a massless scalar field, while the other – to a nonlinear spinor field. The interaction between the spinor and scalar fields can lead to elimination of singularity of the wave function. There is a possibility of existence of a discrete spectrum of the quantum Universe, as well as tunneling from the region with a rigorous equation of state to the region of the de Sitter vacuum.     

Electron-positron pair and photon generation from vacuum in a de sitter space

Electron-positron pair and photon generation from vacuum is considered for a de Sitter space. The amplitude is calculated in the lowest order of perturbation theory with respect to the radiation interaction. The initial and final vacuum states of the quantized spinor field are taken as those of an adiabatic Bunch-Davis vacuum. The amplitude is shown to be zero, i.e., an adiabatic vacuum in a de Sitter space is stable with respect to radiation. Biya Technological Institute, Polzunov Altai State Technological University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 85–89, October, 1998.     

Static Plane-Symmetric Nonlinear Spinor and Scalar Fields in GR

We consider a system of minimally coupled nonlinear spinor and scalar fields within the scope of a plane-symmetric gravitational field. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The change of the sign of the scalar field energy density of the system in question realizes physically if and only if the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. The choice of spinor field nonlinearity leads to the elimination of scalar field contribution to the metric functions, but leaves its contribution to the total energy unaltered. The spinor field is more sensitive to the gravitational field than the scalar field.     

Vacuum expectation values of the energy-momentum tensor of quantized fields on manifolds with different topologies and geometries. III

In a continuation of the earlier work [1, 2] into vacuum effects of quantized fields on bounded manifolds, the case of a spinor field is considered. The question of the boundary conditions for the Dirac equation is studied. Analytic results are obtained for a number of configurations. A comparison is made with the case of boson fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 9–13, July, 1980.     

Vacuum radiational processes in pair-generating fields

Diverse vacuum radiational processes in a constant homogeneous field are considered from the point of view of QED with an external pair-generating field. Computations are performed for the scalar and spinor versions of the theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 10–12, September, 1982.     

Evolution of mixed particles interacting with classical sources

Systems of scalar and spinor particles that underwent mixing and which originated from external classical sources were investigated. Particle wave functions that take exactly into account external sources were obtained on the basis of solving Lorentz-invariant wave equations in four-dimensional space. Sources localized in space that emit harmonic radiation were considered. It was found that, owing to the presence of vacuum mixing, the scalar and spinor fields in question might oscillate—that is, go over to one another. It was shown that this phenomenon was analogous to neutrino flavor oscillations in a vacuum, since the calculated transition probabilities were coincidentwith their counterparts for neutrino oscillations. The situation of an arbitrarymassmatrix (that is, that which involved bothDirac andMajoranamass terms) was studied for the case of spinor-field evolution. The possibility of the appearance of antiparticles in a beam that originally involved only particles was analyzed. The question of whether the use of this method in describing neutrino flavor oscillations is legitimate was studied.     

Dirac Field on Moyal-Minkowski Spacetime and Non-commutative Potential Scattering

The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyal-deformed multiplication with respect to the spatial variables. The Moyal-deformed multiplication corresponds to the product of the algebra of a Moyal plane described in the setting of spectral geometry. It will be explained how this leads to an interpretation of the Dirac field as a quantum field theory on Moyal-deformed Minkowski spacetime (with commutative time) in a setting of Lorentzian spectral geometries of which some basic aspects will be sketched. The scattering transformation will be shown to be unitarily implementable in the canonical vacuum representation of the Dirac field. Furthermore, it will be indicated how the functional derivatives of the ensuing unitary scattering operators with respect to the strength of the non-commutative potential induce, in the spirit of Bogoliubov’s formula, quantum field operators (corresponding to observables) depending on the elements of the non-commutative algebra of Moyal-Minkowski spacetime.     

Thick brane solutions supported by two spinor fields

Stationary thick brane solutions supported by two spinor fields are considered. Two spinor fields are used here to exclude the off-diagonal components of the energy-momentum tensor of the spinor fields. The trapping of a test scalar field on the brane is also considered.     

VACUUM SOLUTIONS OF CONFORMALLY COVARIANT NONLINEAR COUPLED EQUATIONS

The instantonlike and meronlike vacuum solutions of conformally covariant nonlinear coupled scalar and spinor field equations are discussed.     

Flat limit of the de Sitter QFT in the rest frame vacuum

The problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is considered in the traditional adiabatic vacuum and in the new rest frame vacuum we proposed recently,in which the frequencies are separated in the rest frames as in special relativity.It is shown that only in the rest frame vacuum can the Minkowskian flat limit be reached naturally fbr any momentum,whereas in the adiabatic vacuum,this limit remains undefined in rest frames in which the momentum vanishes.An important role is played by the phases of the fundamental solutions in the rest frame vacuum,which must be regularized to obtain the desired Minkowskian flat limits.This procedure fixes the phases of the scalar mode functions and Dirac spinors,resulting in their definitive expressions derived here.The physical consequenee is that,in the rest frame vacuum,the flat limits of the oneparticle operators are simply the corresponding operators of special relativity.     

Effective Lagrangian for general relativity in presence of a quantized scalar field

New correction terms induced by a quantized scalar field vacuum on the Lagrangian of general relativity are investigated in case of an Einstein universe.     

A homogeneous multicomponent cosmological model with interacting spinor,scalar, and vector fields in the presence of dark energy

The evolution of a homogeneous multicomponent cosmological model with interacting spinor, vector, and scalar fields in the presence of dark energy described by the ideal liquid with the corresponding state equation is considered. The source of the vector and spinor fields is the kinetic energy of the inflation (scalar) field that is modeled by introduction of Lagrangians for the spinor and vector fields interacting with the scalar field through the squared gradient. A system of the dynamic Einstein–Proca–Klein–Fock and ideal liquid equations in the presence of interaction of the cosmological model components is solved. The role of individual components in the process of model evolution is elucidated.     

Interacting Spinor and Scalar Fields in Bianchi Type I Universe Filled with Perfect Fluid: Exact Self-Consistent Solutions

In the framework of Bianchi I (BI) cosmological models a self-consistent system of interacting spinor and scalar fields has been considered. We introduced an interaction function F(I, J) which is an arbitrary function of invariants I and J, generated from the real bilinear forms of the spinor field. Exact self-consistent solutions to the field equations have been obtained for the cosmological model filled with perfect fluid. The initial and the asymptotic behavior of the field functions and of the metric one has been thoroughly studied.     

Spinor model of a perfect fluid

Different characteristics of matter influencing the evolution of the uUniverse haves been simulated by means of a nonlinear spinor field. We have considered two cases where the spinor field nonlinearity occurs either as a result of self-action or due to the interaction with a scalar field.     

Smoothing regularization and particle creation in curved spacetime

A regularization procedure is given for the stress tensor of a quantized field in a background metric. This regularization is shown to be equivalent to a covariant renormalization of constants in the generalized Einstein equations. An example of the massive spinor field in Robertson-Walker universe is considered. Regular values of the stress tensor near the cosmological singularity are found.