Linear spin-zero quantum fields in external gravitational and scalar fields

The quantum theory of both linear, and interacting fields on curved space-times is discussed. It is argued that generic curved space-time situations force the adoption of the algebraic approach to quantum field theory: and a suitable formalism is presented for handling an arbitrary quasi-free state in an arbitrary globally hyperbolic space-time.For the interacting case, these quasi-free states are taken as suitable starting points, in terms of which expectation values of field operator products may be calculated to arbitrary order in perturbation theory. The formal treatment of interacting fields in perturbation theory is reduced to a treatment of free quantum fields interacting with external sources.Central to the approach is the so-called two-current operator, which characterises the effect of external sources in terms of purely algebraic (i.e. representation free) properties of the source-free theory.The paper ends with a set of Feynman rules which seems particularly appropriate to curved space-times in that it takes care of those aspects of the problem which are specific to curved space-times (and independent of interaction). Heuristically, the scheme calculates in-in rather than in-out matrix elements. Renormalization problems are discussed but not treated.Work partly supported by the Schweizerische Nationalfonds     

Galilean-invariant scalar fields can strengthen gravitational lensing

The mystery of dark energy suggests that there is new gravitational physics on long length scales. Yet light degrees of freedom in gravity are strictly limited by Solar System observations. We can resolve this apparent contradiction by adding a Galilean-invariant scalar field to gravity. Called Galileons, these scalars have strong self-interactions near overdensities, like the Solar System, that suppress their dynamical effect. These nonlinearities are weak on cosmological scales, permitting new physics to operate. In this Letter, we point out that a massive-gravity-inspired coupling of Galileons to stress energy can enhance gravitational lensing. Because the enhancement appears at a fixed scaled location for dark matter halos of a wide range of masses, stacked cluster analysis of weak lensing data should be able to detect or constrain this effect.     

Calculating the probabilities of quantum processes in external gravitational fields. I.

A method is proposed for calculating the amplitudes of quantum processes for a synchronous and sealer field in warped space-time. It is shown that these amplitudes can be expressed in terms of the matrix elements of the Green functions of the field equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 90–95, March, 1979.The authors thank V. P. Frolov for stimulating discussions on the problems referred to in the paper.     

Method of calculating probabilities of quantum processes in external gravitational fields. II

A method is proposed for calculating amplitudes of arbitrary quantum processes in curved space-time for a system of interacting fields. A generalization of the diagram technique is presented, which permits the consideration of the situation where the initial and final vacuum states are different.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 55–61, April, 1979.The authors are grateful to V. P. Frolov for critical comments.     

Impact of spin-zero particle-photon interactions on light polarization in external magnetic fields

If the recent PVLAS results on polarization changes of a linearly polarized laser beam passing through a magnetic field are interpreted by an axion-like particle, it is almost certain that it is not a standard QCD axion. Considering this, we study the general effective interactions of photons with spin-zero particles without restricting the latter to be a pseudo-scalar or a scalar, i.e., a parity eigenstate. At the lowest order in effective field theory, there are two dimension-5 interactions, each of which has previously been treated separately for a pseudo-scalar or a scalar particle. By following the evolution in an external magnetic field of the system of spin-zero particles and photons, we compute the changes in light polarization and the transition probability for two experimental set-ups: one-way propagation and round-trip propagation. While the first may be relevant for astrophysical sources of spin-zero particles, the second applies to laboratory optical experiments like PVLAS. In the one-way propagation, interesting phenomena can occur for special configurations of polarization where, for instance, transition occurs but light polarization does not change. For the round-trip propagation, however, the standard results of polarization changes for a pseudoscalar or a scalar are only modified by a factor that depends on the relative strength of the two interactions.     

Relativistic particle dynamics in external gravitational fields

Using the Riemann metric for event space, which leads to Newtonian mechanics at nonrelativistic velocities and not necessarily weak gravitational fields, the dynamics of relativistic particles in external gravitational fields are considered. Trajectories, laws of motion, and equations of light rays are found in homogeneous and Newtonian fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 56–61, October, 1977.In conclusion the authors thank Yu. G. Pavlenko for his evaluation of the results and valuable advice.     

Intrinsic gravitational regularization of quantum fields

One implication of maximal proper acceleration is an intrinsic regularization of quantum fields which depends on the universal gravitational constant. It also follows that the vacuum energy density, seen by any one observer, is finite.     

Linearization stability of coupled gravitational and scalar fields in asymptotically flat space-times

Using the methods of Choquet-Bruhat, Fischer and Marsden and using weighted Sobolev spaces developed recently by Christodoulou and Choquet-Bruhat, it is proved that the Einstein field equations coupled with self-gravitating scalar fields are linearization stable in asymptotically flat space-times.     

Homogeneous and isotropic solutions of a gravitational theory with scalar fields

We study the homogeneous and isotropic solutions of a gravitational theory with scalar fields. Qualitative characteristics of these solutions are analyzed and important differences with respect to the usual Einstein theory are pointed out.     

Five-dimensional theory of interacting scalar,electromagnetic, and gravitational fields

An (n+1) factorization of an (n+1)-dimensional Riemann manifold is performed. For a space permitting a Killing vector, the (n+l)-dimensional Hubert variational principle reduces to the variational principle for the corresponding quantities in an n-dimensional space. Hence, setting n=4 and n=3, versions of a unified theory of gravitational, electromagnetic, and scalar fields and the steady-space theory of general relativity theory, respectively, are constructed. The five-dimensional variational principle for geodesics reduces to the four-dimensional leastaction principle for the test charged particle moving in gravitational, electromagnetic, and scalar fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 58–65, November, 1979.     

Static spheres — Sources of scalar,electromagnetic, and gravitational fields

Static sources of scalar, electromagnetic, and gravitational fields are considered within the theory of general relativity and within the class of scalar-tensor gravitation theories. From the conditions of regularity and nonnegativeness of matter density a number of limitations on the possible model parameters are obtained. An example of a regular model in general relativity is presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 51–56, October, 1977.     

Out-of-equilibrium quantum field dynamics in external fields

The quantum dynamics of the symmetry-broken λ(Φ ²)² scalar-field theory in the presence of an homogeneous external field is investigated in the large-N limit. We consider an initial thermal state of temperature T for a constant external field J. A subsequent sign flip of the external field, J→ - J, gives rise to an out-of-equilibrium nonperturbative quantum field dynamics. We review here the dynamics for the symmetry-broken λ(Φ ²)² scalar N component field theory in the large-N limit, with particular stress in the comparison between the results when the initial temperature is zero and when it is finite. The presence of a finite temperature modifies the dynamical effective potential for the expectation value, and also makes that the transition between the two regimes of the early dynamics occurs for lower values of the external field. The two regimes are characterized by the presence or absence of a temporal trapping close to the metastable equilibrium position of the potential. In the cases when the trapping occurs it is shorter for larger initial temperatures.     

Relativistic quantum mechanics of spin-zero and spin-half particles

We consider the quantum mechanics of directly interacting relativistic particles of spin-zero and spin-half. We introduce a scalar product in the vector space of physical states which is finite, positive definite and relativistically invariant and keeps orthogonal eigenstates of total four momentum belonging to different eigenvalues. This allows us to show that the vector space of physical states is, in fact, a Hilbert space. The case of two particles is explicitly considered and the Cauchy problem of physical wave function illustrated. The problem of a spin-1/2 particle interacting with a spin-zero particle is considered and a new equation is proposed for two spin-1/2 particles interacting via the most general form of interaction possible. The restrictions due to Hermiticity, space inversion and time reversal invariance are also considered.     

Free fall of a spin-zero quantum particle

The acceleration operators are derived for a spin-zero quantum particle near an observation point which is at rest in a static, spherically symmetric gravitational field. The expectation value of the acceleration of the center of gravity of an arbitrary wave packet is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 36–41, June, 1976.     

Foundations of the unified theory of gravitational,electromagnetic, and scalar fields

A particular case of bimetrical unified field theory is considered, which is based on Hilbert's proposal of obtaining a complete system of independent equations for unified theory. The action depends on two symmetrical tensors g_μν and g _μν ^° , the second leading to a zero curvature tensor, which results in the theory being invariant under the Poincaré group, and in ten conservation laws. The field equations obtained when varying the action with respect to g_μν have the form of Einstein equations whose righthand side is not defined independently, but is rather a function of g_μν and g _μν ^° . The vector and scalar gauge transformations corresponding to variations δS of special form are defined. With the aid of these transformations, the electromagnetic and scalar fields are introduced within the framework of the unified theory. The basic equations of the theory under consideration contain a new dimensional physical constant, which connects gravitation and electromagnetism. A numerical estimate of this constant is given.     

Quantum pseudodots under the influence of external vector and scalar fields

We study the spherical quantum pseudodots in the Schr o¨dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility, and the persistent currents are also studied by using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.     

Effective potential for quantum scalar fields in a de Sitter geometry

We study the quantum theory of an O(N) scalar field on de Sitter geometry at leading order in a nonperturbative 1/N expansion. This resums the infinite series of so-called superdaisy loop diagrams. We obtain the de Sitter symmetric solutions of the corresponding, properly renormalized, dynamical field equations and compute the complete effective potential. Because of its self-interactions, the field acquires a strictly positive square mass which screens potential infrared divergences. Moreover, strongly enhanced ultralong-wavelength fluctuations prevent the existence of a spontaneously broken symmetry state in any dimension.     

A static spherically symmetric solution for interacting scalar,electromagnetic, and gravitational fields

A unified theory of interacting scalar, electromagnetic, and gravitational fields constructed in previous papers by the author is used in considering a static spherically symmetrical case. An effective one-dimensional Lagrangian is derived together with the corresponding Hamilton-Jacobi equation. The solution to this equation is used in deriving a solution to Einstein's equations for the initial system of interacting fields. Some consequences of the solution are examined. A relationship is derived between the constants of integration that ensures finiteness in the total field energy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 74–80, March, 1980.I am indebted to Yu. S. Vladimirov and V. N. Mel'nikov, as well as other participants in the seminar of the Gravitation Section of the Ministry of Technical Colleges of the USSR, for their interest and valuable comments.