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V. E. Rochev

Publications and source records attributed to V. E. Rochev.

At least 19 recordsLinked to original sources
arXiv2018

On the phase structure of vector-matrix scalar model in four dimensions

The leading-order equations of the $1/N$ -- expansion for a vector-matrix model with interaction $gϕ_a^*ϕ_bχ_{ab}$ in four dimensions are investigated. This investigation shows a change of the asymptotic behavior in the deep Euclidean region in a vicinity of a certain critical value of the coupling constant. For small values of the coupling the phion propagator behaves as free. In the strong-coupling region the asymptotic behavior drastically changes -- the propagator in the deep Euclidean region tend to some constant limit. The phion propagator in the coordinate space has a characteristic shell structure. At the critical value of coupling that separates the weak and strong coupling regions, the asymptotic behavior of the phion propagator is a medium among the free behavior and the constant--type behavior in strong--coupling region. The equation for a vertex with zero transfer is also investigated. The asymptotic behavior of the solutions shows the finiteness of the charge renormalization constant. In the strong-coupling region, the solution for the vertex has the same shell structure in coordinate space as the phion propagator. An analogy between the phase transition in this model and the re-arrangement of the physical vacuum in the supercritical external field due to the "fall-on-the-center" phenomenon is discussed.

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arXiv2018

Asymptotic behavior and critical coupling in scalar Yukawa model

The solution of the equation for the phion propagator in the leading order of the $1/N$ -- expansion for a vector-matrix model with interaction $g(ϕ_a)^*ϕ_bχ_{ab}$ in four dimensions shows a change of the asymptotic behavior in the deep Euclidean region in a vicinity of a certain critical value of the coupling constant.

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arXiv2015

Hermitian vs PT-Symmetric Scalar Yukawa Model

A comparative analysis of a model of complex scalar field $ϕ$ and real scalar field $χ$ with interaction $gϕ^*ϕχ$ for the real and purely imaginary values of coupling $g$ in perturbative and non-perturbative regions. In contrast to the usual Hermitian version (real $g$), which is asymptotically free and energetically unstable, the non-Hermitian $PT$--symmetric theory (imaginary $g$) is energetically stable and not asymptotically free. The non-perturbative approach based on Schwinger--Dyson equations reveals new interesting feature of the non-Hermitian model. While in the Hermitian version of theory the phion propagator has the non-physical non-isolated singularity in the Euclidean region of momenta, the non-Hermitian theory substantially free of this drawback, as the singulatity moves in the pseudo-Euclidean region.

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arXiv2012

Asymptotic behavior in a model with Yukawa interaction from Schwinger-Dyson equations

A system of Schwinger-Dyson equations for pseudoscalar four-dimensional Yukawa model in the two-particle approximation is investigated. The simplest iterative solution of the system corresponds to the mean-field approximation (or, equivalently, to the leading order of 1/N-expansion) and includes a non-physical Landau pole in deep-Euclidean region for the pseudoscalar propagator $Δ$. It is argued, however, that a full solution may be free from non-physical singularities and has the self-consistent asymptotic behavior $p^2_eΔ\simeq C\,\log^{-4/5}\frac{p^2_e}{M^2}$. An approximate solution confirms the positivity of $C$ and the absence of Landau pole.

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arXiv2011

Asymptotic behavior in the scalar field theory

An asymptotic solution of the system of Schwinger-Dyson equations for four-dimensional Euclidean scalar field theory with interaction $\fracλ{2}(ϕ^*ϕ)^2$ is obtained. For $λ>λ_{cr}=16π^2$ the two-particle amplitude has the pathology-free asymptotic behavior at large momenta. For $λ<λ_{cr}$ the amplitude possesses Landau-type singularity.

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arXiv2009

Properties of predictive formulation of the Nambu-Jona-Lasinio model and ghost problem

Recently proposed by Battistel et al. "predictive formulation of the NJL model" is discussed and its connection with the differential regularization is noted. The principal problem of this formulation is a non-physical singularity (Landau pole) in meson propagators. A modification of the formulation, which is free of the Landau pole and conserves main features of the approach, is proposed.

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arXiv2006

On multi-particle functions and pion-decay constant in Nambu--Jona-Lasinio model

The system of second-order equations of mean-field expansion is considered for Nambu--Jona-Lasinio model with chiral symmetry of SU(2)-group. The system includes equations for four-particle and three-particle functions and also equations for next-to-leading two-particle function and next-to-next-to-leading quark propagator. Exact solutions for four-particle and three-particle equations are obtained. The solution for four-particle function is a disconnected combination of the leading-order two-particle functions. The connected part of three-particle function includes two-meson and three-meson contributions. The solution of three-particle equation permits to close the equation for next-to-leading two-particle function and to calculate a correction to pion-decay constant $f_π$. This correction increases from 14% to 28% when values of quark condensate varies from $-(210 MeV)^3$ to $-(250 MeV)^3$.

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arXiv2006

Two regularizations - two different models of Nambu-Jona-Lasinio

Two variants of the Nambu--Jona-Lasinio model -- the model with 4-dimensional cutoff and the model with dimensionally-analytical regularization -- are systematically compared. It is shown that they are, in essence, two different models of light-quark interaction. In the mean-field approximation the distinction becomes apparent in a behavior of scalar amplitude near the threshold. For 4-dimensional cutoff the pole term can be extracted, which corresponds to sigma-meson. For dimensionally-analytical regularization the singularity of the scalar amplitude is not pole, and this singularity is quite disappeared at some value of the regularization parameter. Still more essential distinction of these models exists in the next-to-leading order of mean-field expansion. The calculations of meson contributions in the quark chiral condensate and in the dynamical quark mass demonstrate, that these contributions though their relatively smallness can destabilize the Nambu--Jona-Lasinio model with 4-dimensional cutoff. On the contrary, the Nambu--Jona-Lasinio model with dimensionally-analytical regularization is stabilized with the next-to-leading order, i.e. the value of the regularization parameter shifts to the stability region, where these contributions decrease.

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arXiv2006

On Equations for the Multi-quark Bound States in Nambu--Jona-Lasinio Model

In present report we review some preliminary results of investigation of higher orders of mean-field expansion for Nambu--Jona-Lasinio model. We discuss first results of investigation of next-to-next-to-leading order of mean-field expansion equations for four-quark and three-quark Green functions. We have considered equations for Green functions of Nambu--Jona-Lasinio model in mean-field expansion up to third order.

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arXiv2004

Mean-field expansion and meson effects in chiral condensate of analytically regularized Nambu -- Jona-Lasinio model

Scalar meson contributions in chiral quark condensate are calculated for analytically regularized Nambu -- Jona-Lasinio model in framework of mean-field expansion in bilocal-source formalism. Sigma-meson contribution for physical values of parameters is found to be small. Pion contribution is found to be significant and should be taken into account at the choice of the parameter values.

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arXiv2003

Quantum fluctuations of chiral condensate in the analytically regularized Nambu--Jona-Lasinio model

The problem of quantum fluctuations of the chiral condensate due to next-to-leading contributions is investigated. Meson contributions to the chiral condensate are calculated in the Nambu--Jona-Lasinio model with the analytical (dimensional) regularization in a framework of the mean-field expansion. The pion contribution can be significant, while the sigma-meson contribution is small in the regime of physical values of the model parameters. Non-pole contributions are also estimated and found to be small.

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arXiv2000

On Nonperturbative Calculations in Quantum Electrodynamics

A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach allows one to take into account the gauge invariance conditions (Ward identities) and to perform the renormalization program. The iteration scheme can be realized in two versions. The first one ("perturbative vacuum") corresponds to chain summation in the diagram language. In this version in four-dimensional theory the non-physical singularity (Landau pole) arises which leads to the triviality of the renormalized theory. The second version ("nonperturbative vacuum") corresponds to ladder summation and permits one to make non-perturbative calculations of physical quantities in spite of the triviality problem. For chiral-symmetrical leading approximation two terms of the expansion of the first-step vertex function over photon momentum are calculated. A formula for anomalous magnetic moment is obtained. A problem of dynamical chiral symmetry breaking (DCSB) is considered, the calculations are performed for renormalized theory in Minkowsky space. In the strong coupling region DCSB-solutions arise. For the renormalized theory a DCSB-solution is also possible in the weak coupling region but with a subsidiary condition on the value of $α$.

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arXiv1999

An approach to approximate calculations of Green functions

A new approach proposed recently by author for the calculation of Green functions in quantum field theory and quantum mechanics is briefly reviewed. The method is applied to nonperturbative calculations for anharmonic oscillator, $ϕ^4$-theory, quantum electrodynamics and other models.

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arXiv1999

A mechanism for dynamical generation of SU(2) Georgi-Glashow model

A mechanism for the dynamical mass generation of a non-Abelian gauge field which is based on taking into account the contributions of the gauge field vacuum configurations into the formation of the physical vacuum is considered. For a model of the physical vacuum as a superposition of Abelian configurations the gauge field propagator is calculated in the leading order of $1/d$-expansion ($d$ is a space-time dimension). One-particle spectrum of the model corresponds to the gauge sector of SU(2) Georgi-Glashow model.

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arXiv1998

On Higgs mechanism in non-perturbative region

A generalization of the Higgs mechanism is considered which takes into account the contributions of gauge field vacuum configuration into the formation of the physical vacuum. For the Abelian Higgs model the triviality bound $m_H\le~1.15m_A$ is found.

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arXiv1997

On solving Schwinger-Dyson equations for non-Abelian gauge theory

A method for solving Schwinger-Dyson equations for the Green function generating functional of non-Abelian gauge theory is proposed. The method is based on an approximation of Schwinger-Dyson equations by exactly soluble equations. For the SU(2) model the first step equations of the iteration scheme are solved which define a gauge field propagator. Apart from the usual perturbative solution, a non-perturbative solution is found which corresponds to the spontaneous symmetry breaking and obeys infrared finite behaviour of the propagator.

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arXiv1997

The four-fermion interaction in D=2,3,4: a nonperturbative treatment

A new nonperturbative approach is used to investigate the Gross-Neveu model of four fermion interaction in the space-time dimensions 2, 3 and 4, the number $N$ of inner degrees of freedom being a fixed integer. The spontaneous symmetry breaking is shown to exist in $D=2,3$ and the running coupling constant is calculated. The four dimensional theory seems to be trivial.

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