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Mikhail N. Smolyakov

Publications and source records attributed to Mikhail N. Smolyakov.

At least 19 recordsLinked to original sources
arXiv2026

Remarks on quantum scalar field theory for a uniformly accelerated reference frame and a Schwarzschild black hole

In the present paper, the cases of a uniformly accelerated reference frame and a Schwarzschild black hole in two and four dimensions are discussed focusing on formal aspects of the corresponding quantum scalar field theories. The main emphasis is made on building consistent quantum field theories and highlighting the problems that are not considered elsewhere. In particular, some pathologies in the case of a uniformly accelerated reference frame are discussed in detail: it is shown that some quantum states that are well defined in Minkowski spacetime possess an infinite energy when considered in Rindler spacetime. In the case of a Schwarzschild black hole in four dimensions, it is shown that the standard theory providing the Unruh vacuum state turns out to be inconsistent. The problem of consistency of quantum scalar field theory in Kruskal-Szekeres spacetime is also discussed.

gr-qc↗
arXiv2025

Peculiarities of quantum field theory in the presence of a wormhole

In this paper, quantum theory of a real massive scalar field in the background of a traversable wormhole is examined. The wormhole is supposed to connect two different universes; as a particular example the simplest Ellis wormhole is considered. It is shown that the resulting theory possesses a doubling of quantum states parametrized by the same value of asymptotic momentum; two different sets of such degenerate states are localized in different universes. This is a consequence of the topological structure of the wormhole spacetime, which is the same as the topological structure of the Schwarzschild spacetime providing a similar degeneracy of quantum states.

gr-qc↗
arXiv2023

Asymptotic behavior of solutions and spectrum of states in the quantum scalar field theory in the Schwarzschild spacetime

In this paper, the study of canonical quantization of a free real massive scalar field in the Schwarzschild spacetime is continued. The normalization constants for the eigenfunctions of the corresponding radial equation are calculated, providing the necessary coefficients for the doubly degenerate scatteringlike states that are used in the expansion of the quantum field. It is shown that one can pass to a new type of states such that the spectrum of states with energies larger than the mass of the field splits into two parts. The first part consists of states that resemble properly normalized plane waves far away from the black hole, so they just describe the theory for an observer located in that area. The second part consists of states that live relatively close to the horizon and whose wave functions decrease when one goes away from the black hole. The appearance of the second part of the spectrum, which follows from the initial degeneracy of the scatteringlike states, is a consequence of the topological structure of the Schwarzschild spacetime.

gr-qc↗
arXiv2023

Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature. II. The general case

In the present paper, discussion of the canonical quantization of a weakly nonideal Bose gas at zero temperature within the framework of the Bogolyubov approach is continued. Contrary to the previous paper on this subject, here the two-body interaction potential is considered in the general form. It is shown that in such a case consideration of the first nonlinear correction also leads to the automatic particle number conservation without any additional assumptions or modification of the resulting effective Hamiltonian.

cond-mat.quant-gas↗
arXiv2022

Some properties of small perturbations against a stationary solution of the nonlinear Schrodinger equation

In this paper, classical small perturbations against a stationary solution of the nonlinear Schrodinger equation with the general form of nonlinearity are examined. It is shown that in order to obtain correct (in particular, conserved over time) nonzero expressions for the basic integrals of motion of a perturbation even in the quadratic order in the expansion parameter, it is necessary to consider nonlinear equations of motion for the perturbations. It is also shown that, despite the nonlinearity of the perturbations, the additivity property is valid for the integrals of motion of different nonlinear modes forming the perturbation (at least up to the second order in the expansion parameter).

math-ph↗
arXiv2022

Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature

In the present paper, quantization of a weakly nonideal Bose gas at zero temperature along the lines of the well-known Bogolyubov approach is performed. The analysis presented in this paper is based, in addition to the steps of the original Bogolyubov approach, on the use of nonoscillation modes (which are also solutions of the linearized Heisenberg equation) for recovering the canonical commutation relations in the linear approximation, as well as on the calculation of the first nonlinear correction to the solution of the linearized Heisenberg equation which satisfies the canonical commutation relations at the next order. It is shown that, at least in the case of free quasi-particles, consideration of the nonlinear correction automatically solves the problem of nonconserved particle number, which is inherent to the original approach.

cond-mat.quant-gas↗
arXiv2019

Perturbations against a Q-ball. II. Contribution of nonoscillation modes

In the present paper, discussion of perturbations against a Q-ball solution is continued. It is shown that in order to correctly describe perturbations containing nonoscillation modes, it is also necessary to consider nonlinear equations of motion for the perturbations, like in the case of oscillation modes only. It is also shown that the additivity of the charge and the energy of different modes holds for the most general nonlinear perturbation consisting of oscillation and nonoscillation modes.

hep-th↗
arXiv2018

Perturbations against a Q-ball: Charge, energy, and additivity property

In the present paper, perturbations against a Q-ball solution are considered. It is shown that if we calculate the U(1) charge and the energy of the modes, which are solutions to linearized equations of motion, up to the second order in perturbations, we will get incorrect results. In particular, for the time-dependent modes we will obtain nonzero terms, which explicitly depend on time, indicating the nonconservation over time of the charge and the energy. It is shown that, as expected, this problem can be resolved by considering nonlinear equations of motion for the perturbations, providing second-order corrections to the solutions of linearized equations of motion. It turns out that contributions of these corrections to the charge and the energy can be taken into account without solving explicitly the nonlinear equations of motion for the perturbations. It is also shown that the use of such nonlinear equations not only recovers the conservation over time of the charge and the energy but also results in the additivity of the charge and the energy of different modes forming the perturbation.

hep-th↗
arXiv2016

Fermions in five-dimensional brane world models

In the present paper the fermion fields, living in the background of five-dimensional warped brane world models with compact extra dimension, are thoroughly examined. The Kaluza-Klein decomposition and isolation of the physical degrees of freedom is performed for those five-dimensional fermion field Lagrangians, which admit such a decomposition to be performed in a mathematically consistent way and provide a physically reasonable four-dimensional effective theory. It is also shown that for the majority of five-dimensional fermion field Lagrangians there are no (at least rather obvious) ways to perform the Kaluza-Klein decomposition consistently. Moreover, in these cases one may expect the appearance of various pathologies in the four-dimensional effective theory. Among the cases, for which the Kaluza-Klein decomposition can be performed in a mathematically consistent way, the case, which reproduces the Standard Model by the zero Kaluza-Klein modes most closely regardless of the size of the extra dimension, is examined in detail in the background of the Randall-Sundrum model.

hep-th↗
arXiv2016

Some problems with reproducing the Standard Model fields and interactions in five-dimensional warped brane world models

In the present paper we examine, from the purely theoretical point of view and in a model-independent way, the case, when matter, gauge and Higgs fields are allowed to propagate in the bulk of five-dimensional brane world models with compact extra dimension, and the Standard Model fields and their interactions are supposed to be reproduced by the corresponding zero Kaluza-Klein modes. An unexpected result is that in order to avoid possible pathological behavior in the fermion sector, it is necessary to impose constraints on the fermion field Lagrangian. In the case when the fermion zero modes are supposed to be localized at one of the branes, these constraints imply an additional relation between the vacuum profile of the Higgs field and the form of the background metric. Moreover, this relation between the vacuum profile of the Higgs field and the form of the background metric results in the exact reproduction of the gauge boson and fermion sectors of the Standard Model by the corresponding zero mode four-dimensional effective theory in all the physically relevant cases, allowed by the absence of pathologies. Meanwhile, deviations from these conditions can lead either back to pathological behavior in the fermion sector or to a variance between the resulting zero mode four-dimensional effective theory and the Standard Model, which, depending on the model at hand, may, in principle, result in constraints putting the theory out of the reach of the present day experiments.

hep-th↗
arXiv2015

Higgs-radion mixing in stabilized brane world models

We consider a quartic interaction of the Higgs and Goldberger-Wise fields, which connects the mechanism of the extra dimension size stabilization with spontaneous symmetry breaking on our brane and gives rise to a coupling of the Higgs field to the radion and its KK tower. We estimate a possible influence of this coupling on the Higgs-radion mixing and study restrictions on model parameters from the LHC data.

hep-ph↗
arXiv2013

More on divergences in brane world models

In this paper a model in a space-time with compact extra dimension is presented, describing five-dimensional fermion fields interacting with an electromagnetic field localized on a brane. This model can be considered as a toy model for examining possible consequences of the localization of gauge fields on a brane. It is shown that in the limit of infinite extra dimension, the lowest-order amplitudes of some processes in the resulting four-dimensional effective theory are divergent. Such a "localization catastrophe" can be inherent to more realistic brane world models with infinite extra dimensions.

hep-th↗
arXiv2012

On unremovable divergencies in four-dimensional electrodynamics localized on a domain wall

In this paper a model describing fermions and gauge field localized on a domain wall is considered. The zero-mode sector of the model reproduces four-dimensional spinor electrodynamics. It is shown that in the resulting four-dimensional effective theory the lowest-order renormalized amplitude of the elastic $γγ$ scattering process is divergent due to the contributions of higher modes and thus such a scenario can not be considered as a realistic mechanism for fields localization on a domain wall.

hep-th↗
arXiv2010

Bulk metric of brane world models and submanifolds in 6D pseudo-Euclidean space-time

In this short note, five-dimensional brane world models with dS_{4} metric on the branes are discussed. The explicit coordinate transformations, which show the equivalence between the bulk metric of these brane world models and the metric induced on an appropriate submanifolds in the flat six-dimensional pseudo-Euclidean space-time, are presented. The cases of the zero and non-zero cosmological constant in the bulk are discussed in detail.

gr-qc↗