The Green formula in the theory of potential scattering and corrections to the eikonal scattering amplitude

A method based on the Green formula is developed for calculating the scattering amplitude of fast charged particles in an external field. The scattering amplitude is representable as an integral over an arbitrary closed surface enveloping the domain of influence of the external field on the particle. Corrections to the eikonal scattering amplitude are simply derived without using the specific form of the potential. The resulting formulas can be used to investigate the interaction between particles and fields of complex configuration. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. No. 2, pp. 280–288, May, 1998.     

Wave function and the probability current distribution for a bound electron moving in a uniform magnetic field

We study the effects of electromagnetic fields on nonrelativistic charged spinning particles bound by a short-range potential. We analyze the exact solution of the Pauli equation for an electron moving in the potential field determined by the three-dimensional δ-well in the presence of a strong magnetic field. We obtain asymptotic expressions for this solution for different values of the problem parameters. In addition, we consider electron probability currents and their dependence on the magnetic field. We show that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account. The obtained dependences of the current distribution, which is an experimentally observable quantity, can be manifested directly in scattering processes, for example.     

Functional integrals and phase stability properties in the $$O(N)$$ vector field condensation model

Theoretical and Mathematical Physics - Using condensation of auxiliary Bose fields and the functional integral method, we derive an effective action of the binary $$O(N)$$ vector field model on a...     

Quantum Entanglement in the Nonrelativistic Collision Between Two Identical Fermions with Spin 1/2

Theoretical and Mathematical Physics - In the framework of nonstationary scattering theory, we study the formation of an entangled state of two identical nonrelativistic spin-1/2 particles as a...     

Thermal quantum fields with spatially cutoff interactions in 1+1 space-time dimensions

We construct interacting quantum fields in 1+1 space-time dimensions, representing charged or neutral scalar bosons at positive temperature and zero chemical potential. Our work is based on prior work by Klein and Landau and Høegh-Krohn. Generalized path space methods are used to add a spatially cutoff interaction to the free system, which is described in the Araki-Woods representation. It is shown that the interacting KMS state is normal w.r.t. the Araki-Woods representation. The observable algebra and the modular conjugation of the interacting system are shown to be identical to the ones of the free system and the interacting Liouvillean is described in terms of the free Liouvillean and the interaction.     

COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R~3

The compressible non-isentropic bipolar Navier-Stokes-Poisson (BNSP) system is investigated in R 3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in H l (R 3 ) ∩ Bs 1,1 (R 3 ) for l ≥ 4 and s ∈ (0, 1], it is shown that the density and temperature for each charged particle (like electron or ion) decay at the same optimal rate (1 + t) 3 4 , but the momentum for each particle decays at the optimal rate (1 + t) 1 4 s 2 which is slower than the rate (1 + t) 3 4 s 2 for the compressible Navier-Stokes (NS) equations [19] for same initial data. However, the total momentum tends to the constant state at the rate (1+t) 3 4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.     

Electrohydrodynamic flow in a retarding electric field with allowance for charged particle inertia : PMM vol. 43, no. 6, 1979, pp. 1029–1039

The one-dimensional electrohydrodynamic flow is considered in a retarding electric field when, owing to the inertia of charged particles, it is necessary to use the complete equation of momenta for the charged component. It is shown that in spite of the negligibly small relative volume occupies by particles in the initial cross section of the stream, there is a section in which particles move at low but finite velocity with a finite relative volume of the charged component, when the particles are retarded by an external homogeneous electric field (without taking into account the induced field). Interaction of the charged and neutral components, which may be absent in the initial cross section, is always substantial. The pressure drop required for such flow is determined. The flow is investigated with allowance for induced electric fields that diminish the effect of concentration increase of charged particles.     

Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields

A representation in the form of a functional integral is obtained for the partition function of the inhomogeneous 2D Ising model on a triangular lattice where the coupling parameters are arbitrary functions of coordinates. The method for transforming the partition function into an integral uses an auxiliary six-component Grassmann field in which the Grassmann fields corresponding to one of the components commute with the others. Thus, one pair of components realizes a representation of the q-deformed group SL_q(2, R) with q=–1 and the other two pairs correspond to the usual Grassmann spinors (q=1). An explicit expression in terms of the modified Pfaffian is found for the Gaussian integral over these fields and its relation to the ordinary Grassmann functional integral is established.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 441–463, December, 1996.     

q-Deformed grassmann fields and the two-dimensional Ising model

We construct an exact representation of the Ising partition function in the form of the SL_q(2, R)-invariant functional integral for the lattice-free q-fermion field theory (q=–1). It is shown that the q-fermionization allows one to rewrite the partition function of the eight-vertex model in an external field through a functional integral with four-fermion interaction. To construct these representations, we define a lattice (l, q, s)-deformed Grassmann bispinor field and extend the Berezin integration rules to this field. At q=–1, l=s=1, we obtain the lattice q-fermion field which allows us to fermionize the two-dimensional Ising model. We show that the Gaussian integral over (q, s)-Grassmann variables is expressed through the (q, s)-deformed Pfaffian which is equal to square root of the determinant of some matrix at q=±1, s=±1.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 3, pp. 388–412. June, 1995.     

Multitime propagators and the consistency condition

Theoretical and Mathematical Physics - For a nonrelativistic quantum system of $$N$$ particles, the wave function is a function of $$3N$$ spatial coordinates and one temporal coordinate. The...     

Hawking Radiation of Relativistic Particles from Black Strings

Theoretical and Mathematical Physics - We study Hawking radiation of relativistic particles from uncharged and charged black strings in 3+1 dimensions in detail. We use the method of quantum...     

Partially Classical Limit of the Nelson Model

We consider the Nelson model which describes a quantum system of nonrelativistic identical particles coupled to a possibly massless scalar Bose field through a Yukawa type interaction. We study the limiting behaviour of that model in a situation where the number of Bose excitations becomes infinite while the coupling constant tends to zero. In that limit the appropriately rescaled Bose field converges in a suitable sense to a classical solution of the free wave or Klein-Gordon equation depending on whether the mass of the field is zero or not, the quantum fluctuations around that solution satisfy the wave or Klein-Gordon equation and the evolution of the nonrelativistic particles is governed by a quantum dynamics with an external potential given by the previous classical solution. Communicated by Vincent Rivasseau submitted 20/01/05, accepted 23/01/05     

Generalized Electrodynamics With Ternary Internal Structure

In Refs. [2]–[7] we suggested generalized dynamic equations of motion of relativistic charged particles inside electromagnetic fields. The dynamic equations had been formulated in terms of external as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, had been derived from evolution equations for internal momenta. In this paper, along with relativistic dynamics we generalize electromagnetic fields within the scope of ternary algebras. The full theory is constructed in 4D euclidean space. This space possesses an advantage to build ternary mappings from three vectors onto one. The dynamics is given by non-linear evolution equations with cubic characteristic polynomial. In polar representation the internal momenta obey the Jacobi equations whereas external momenta obey the Weierstrass equations for elliptic functions. The generalized electromagnetic fields are defined by the triple fields where the first one has properties of the electric field and the other two have properties of the magnetic field. The field equations for the triple fields analogous to the Maxwell equations are suggested.     

Electron zitterbewegung in a linear crystal with alternating parity

It is shown thatin a linear periodic chain at whose sites electron wave functions of opposite parities alternate the existence of zitterbewegung of a nonrelativistic electron can be established without passage to the limiting case of a continuum. An analogy is established with the relations obtained earlier by the authors for the motion of a nonrelativistic electron in a two-site system. The zitterbewegung of the nonrelativistic electron in the considered system is given an interpretation analogous to the interpretation obtained by the first two authors for the zitterbewegung of a relativistic electron in Dirac's theory. A connection between the energy and effective mass of the nonrelativistic electron in the considered system is established.Institute of Metal Physics, Urals Branch of the Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 2, pp. 343–352, February, 1993.     

Dirac equation in the foldy-wouthuysen representation describing the interaction of spin-1/2 relativistic particles with an external electromagnetic field

The Dirac equation is derived in the Foldy-Wouthuysen representation describing the interaction of spin-1/2 relativistic particles with an external electromagnetic field; it is valid in the weak-field approximation. In contrast to previous studies, this equation includes all of the order derivatives of the field potentials. The quantum-mechanical equation is obtained for the spin motion in the Foldy-Wouthuysen representation; it is consistent with the classical Bargmann-Michel-Telegdi equation.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 1, pp. 46–54, October, 1995.     

Path-integral formulation of backward and umklapp scattering for one-dimensional spinless fermions

We present a (1+1)-dimensional fermionic quantum field theory with nonlocal couplings between currents. This model describes an ensemble of spinless fermions interacting through forward, backward, and UMKLAPP scattering processes. We express the vacuum-to-vacuum functional in terms of a nontrivial fermionic determinant. Using path-integral methods, we find a bosonic representation for this determinant and an effective action depending on three scalar fields, of which two correspond to the physical collective excitations and one is an auxiliary field, which can be integrated out using an approximation technique. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 3, pp. 488–496, March, 1999.     

Transport equations with disparate advection fields. Application to the gyrokinetic models in plasma physics

The subject matter of this paper concerns the asymptotic regimes for transport equations with advection fields having components of very disparate orders of magnitude. The main purpose is to derive the limit models: we justify rigorously the convergence towards these limit models and we investigate the well-posedness of them. Such asymptotic analysis arises in the magnetic confinement context, where charged particles move under the action of strong magnetic fields. In these situations we distinguish between a slow motion driven by the electric field and a fast motion around the magnetic lines.     

Fermions in strong external fields in 2+1 and 1+1 dimensions

The creation of electron-positron pairs from a vacuum by an external Coulomb field is examined within (2+1)-dimensional quantum electrodynamics. If the electromagnetic coupling constant exceeds 0.62 (Z= 85), then in a simple model with a finite-size nucleus, the lower electron level crosses the boundary of the negative-energy continuum (i.e., Dirac sea), and a hole (i.e., positively charged fermion) appears in the negative-energy continuum. An equation is obtained that describes the levels of the ground and excited electron states in a strong Coulomb field of the nucleus. The critical nucleus charge is found for a few lowest electron states. The critical charge in 2+1 dimensions is significantly smaller than in 3+1 dimensions. The problem is reduced to the case of a bounded Coulomb field in 1+1 dimensions without a magnetic field. The interaction of a fermion and an external scalar field in 2+1 and 1+1 dimensions is investigated. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol 122, No. 3, pp. 372–384, March, 2000     

Pauli isotonic oscillatorwith an anomalous magnetic moment in the presence of the Aharonov–Bohm effect: Laplace transform approach

A strong magnetic field significantly affects the intrinsic magnetic moment of fermions. In quantum electrodynamics, it was shown that the anomalous magnetic moment of an electron arises kinematically, while it results from a dynamical interaction with an external magnetic field for hadrons (proton). Taking the anomalous magnetic moment of a fermion into account, we find an exact expression for the boundstate energy and the corresponding eigenfunctions of a two-dimensional nonrelativistic spin-1/2 harmonic oscillator with a centripetal barrier (known as the isotonic oscillator) including an Aharonov–Bohm term in the presence of a strong magnetic field. We use the Laplace transform method in the calculations. We find that the singular solution contributes to the phase of the wave function at the origin and the phase depends on the spin and magnetic flux.