Path integral for a Dirac particle in a quantized plane wave field

The problem of a relativistic spinning particle interacting with a quantized electromagnetic plane wave is treated by employing path integral methods and introducing the notion of a coherent state action. The dynamics of the particle spin is described using the supersymmetric action proposed recently by Alexandrou et al. in the so-called global representation. It is shown that to obtain the relative causal Green function, two fermionic identities, related directly to the classical equations of motion, have to be incorporated. The Green function, as constructed, allows us to extract in a natural way the expressions of the corresponding energy spectrum and wave functions. Received: 26 July 2002 / Revised version: 11 September 2002 / Published online: 25 October 2002     

Exact propagators for Dirac particle with anomalous magnetic moment in a plane wave field

The propagators related to a Dirac particle with anomalous magnetic moment in the presence of a plane wave field are exactly and analytically calculated via the path integral approach in two representations: a global and a local one. It is shown that due to two identities, one bosonic and another fermionic, the path integral calculations are evaluated essentially on classical paths projected along the wave propagation k. Special cases are considered as well. Received: 17 July 2001 / Revised version: 4 October 2001 / Published online: 23 November 2001     

One-dimensional finite motion of a particle in the field of a weak gravitational wave

The Hamiltonian formalism of classical mechanics can be used effectively to describe the motion of a particle (including a massless one) along a segment of material that is in a nonsteady gravitational field. The problem of applying this formalism to the detection of gravitational waves using a Michelson or Fabry—Perot interferometer is considered. The existence of a phase shift of an electromagnetic wave due to the interaction of the electromagnetic and gravitational fields is noted. Moscow State Aviation Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 13–17, August, 1997.     

Dirac particle in a plane wave field and the semi‐classical approximation

In this paper we investigate the influence of photon represented by plane wave field on Dirac particle in the context of path integral approach given by Fradkin and Gitman formalism. In our case, although the action relative to Dirac particle in plane wave field seems to be non quadratic, the result obtained by semi‐classical approach is the same as that found by an exact calculation. Hence; when we add the plane wave field to any quadratic actions related to Fradkin and Gitman approach, the total action behaves like quadratic.     

Dirac particle spin in strong gravitational fields

Dynamics of the Dirac particle spin in general strong gravitational fields is discussed. The Hermitian Dirac Hamiltonian is derived and transformed to the Foldy-Wouthuysen (FW) representation for an arbitrary metric. The quantum mechanical equations of spin motion are found. These equations agree with corresponding classical ones. The new restriction on the anomalous gravitomagnetic moment (AGM) by the reinterpretation of Lorentz invariance tests is obtained.     

Dirac particle in the presence of a plane waveand constant magnetic fields: path integral approach

The Green function (GF) related to the problem of a Dirac particle interacting with a plane wave and constant magnetic fields is calculated in the framework of a path integral via the Alexandrou et al. formalism according to the so-called global projection. As a calculation tool, we introduce two identities (constraints) into this formalism; their main role is the reduction of the dimension of the integral and the emergence in a natural way of some classical paths and, due to the existence of a constant electromagnetic field, we have used the technique of fluctuations. Hence the calculation of the GF is reduced to a known Gaussian integral plus a contribution from the effective classical action.Received: 22 January 2005, Revised: 16 May 2005, Published online: 9 August 2005     

How to lasso a plane gravitational wave

Beginning with the stress-energy tensor of an elastic string this paper derives a relativistic string and its form in a parallel transported Fermi frame including its reduction to a Cosserat string in the Newtonian limit. In a Fermi frame gravitational curvature is seen to induce three dominant relative acceleration terms dependent on: position, velocity and position, strain and position, respectively. An example of a string arranged in an axially flowing ring (a lasso) is shown to have a set of natural frequencies that can be parametrically excited by a monochromatic plane gravitational wave. The lasso also exhibits, in common with spinning particles, oscillations about geodesic motion in proportion to spin magnitude and wave amplitude when the spin axis lies in the gravitational wave front.     

Stochastic quantization method for spinning particles in a gravitational plane wave field

The exact and analytic Green functions for spinning relativistic particles in interaction with a gravitational plane wave field are obtained within the Stochastic Quantization Method of Parisi and Wu. We have separated the classical calculations from those related to the quantum fluctuations. The problem has been solved by using a perturbative treatment via the Langevin equation relying on phase and configuration spaces formulation.      

Quadrupole mass-detector in field of weak plane gravitational fields

A study has been made of the behavior of systems consisting of two test particles joined by a spring (quadrupole mass-detector) and placed in a field of weak plane monochromatic gravitational wave. It was shown that under transverse orientation of the detector the gravitational wave acting on such system sets it into oscillatory motion at a frequency equal to the frequency at which the source of the gravitational wave oscillates. In this case the role of the driving force is played by periodic variations in the equilibrium position with time. The gravitational wave does not act on the detector when it has a longitudinal orientation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 109–114, October, 1978.The author wishes to express his heartfelt gratitude to the participants in the small scientific seminar of the Gravitational Section of the Scientific and Technical Council at the Ministry of Higher Institutes of Learning of the USSR for their interest in the work and valuable critical comments.     

Dirac particles in a gravitational field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle–antiparticle symmetry.     

Charge density wave and weak Kondo effect in a Dirac semimetal CeSbTe

Using angle-resolved photoemission spectroscopy(ARPES) and low-energy electron diffraction(LEED), together with densityfunctional theory(DFT) calculation, we report the formation of charge density wave(CDW) and its interplay with the Kondo effect and topological states in CeSbTe. The observed Fermi surface(FS) exhibits parallel segments that can be well connected by the observed CDWordering vector, indicating that the CDWorder is driven by the electron-phonon coupling(EPC) as a result of the nested FS. The CDW gap is large(～0.3 eV) and momentum-dependent, which naturally explains the robust CDWorder up to high temperatures. The gap opening leads to a reduced density of states(DOS) near the Fermi level(E_F), which correspondingly suppresses the many-body Kondo effect, leading to very localized 4 f electrons at 20 K and above. The topological Dirac cone at the X point is found to remain gapless inside the CDW phase. Our results provide evidence for the competition between CDWand the Kondo effect in a Kondo lattice system. The robust CDWorder in CeSbTe and related compounds provide an opportunity to search for the long-sought-after axionic insulator.     

Resonant generation of plasma oscillations by a plane gravitational wave

An exact solution of the universal Maxwell equations linearized in the amplitude of the induced field is found with the help of a previously found exact solution of the kinetic equation with a model collision integral. Two oscillation modes arise under the action of a gravitational wave in a plasmalike medium: an undamped wave with the frequency of the gravitional wave and a damped one with the plasma frequency. When these frequencies coincide, a resonance arises, as a result of which the amplitude of the electric oscillations increases sharply.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 74–77, January, 1985.     

Dynamics of a charged particle in a progressive plane wave

The dynamics of a charged particle in a relativistic strong electromagnetic plane wave propagating in a medium is studied. The problem is shown to be integrable when the wave propagates in vacuum. When it propagates in plasma, and when the full plasma response is considered, an exhaustive numerical work allows us to conclude that the problem is not integrable.     

Electrically weak fermi particle interaction with a plane wave field taking account of the anomalous magnetic moment

The process of neutrino generation by neutrons n n n(vV)due to interaction of the neutron anomalous magnetic moment with a circularly polarized plane wave field is examined. Using the invariant solution of the generalized Dirac equation, an expression is obtained for the total probability of the process consisting of four contributions. Energetic asymptotics of the results are analyzed and estimates are made of the possibility of observing the effect under laboratory conditions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 91–97, September, 1989.The authors are grateful to V. G. Bagrov for valuable remarks.     

Behavior of a test body in a plane gravitational (gravity) wave

The motion of a test particle in a plane gravity wave characterized by the metricds ²=e ^y c ² dt ² –e ^y dx ² –dy ² –dz ². is considered. It is shown that, in the case of velocities smaller than the velocity of light, when and vary harmonically, the test particle will execute harmonic oscillations along the x, y, and z axes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 112–115, January, 1975.     

Solution of the Dirac equation in plane wave metric backgrounds

We present a new solution of the Dirac equation in the background of a plane wave metric. We examine the relation between sections of the exterior and Clifford bundles of a (pseudo-)Riemannian manifold. A spinor calculus is established and used to investigate a new solution of the Dirac equation lying in a minimal left ideal characterized by a certain idempotent projector.     

Action of weak plane gravitational waves on a system of two connected masses

Based on the monad method of assignment of frames of reference and definitions of observables in the general theory of relativity, an analysis is carried out of the physical interpretation of Weber's formula for the oscillations of elastically connected masses under the action of weak plane gravitational waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 81–86, February, 1979.     

Motion of an ideal fluid in the field of a plane gravitational wave

An exact solution of the equations of relativistic hydrodynamics is found which describes the motion of an initially uniform ideal fluid in the field of a plane gravitational wave of arbitrary amplitude and polarization. For all solutions we find that the pressure and energy density develop singularities on the singular surface, and the velocity of the fluid in the direction of propagation of the gravitational wave approaches the speed of light. In the case of the equation of state =p, the solution becomes intrinsically unstable and describes the generation of sound waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 96–99, November, 1982.