Relativistic quantum particle in a homogeneous external field

The model of the relativistic quantum particle in a homogeneous external field is proposed. This model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space in our case is the one-dimensional Lobachevsky space. We have found the wave functions and propagator for the model under study in both x- and p-representations.     

Relativistic particle in a traveling magnetic field

A Hamiltonian formalism is applied to derive an exact solution to the equation of motion of a charged particle in the electromagnetic field of a traveling current wave. The particle motion is studied in a monochromatic magnetic field and in the traveling jump-like front of the magnetic field, and the wave mechanism for betatron acceleration is analyzed. It is shown that, in each of these situations, a charged particle can be accelerated simultaneously in both the longitudinal and transverse directions.     

DKP particle in time-dependent field

We present the solution of Du.n-Kemmer-Petiau (DKP) equation of spin 0 and 1 in the case of the time-dependent mass in the presence of a time-dependent linear scalar field. Calculation is carried out analytically, the wave functions are then deduced for both cases and are connected respectively to the auxiliary equations. The adiabatic approximation is deduced and reveals that in this study we have an obvious absence of the geometrical amplitude factor.     

Relativistic spinning particle in a gravitational field with torsion

A model of a relativistic spinning particle in a gravitational field with a flat metric and a constant torsion is analyzed within the framework of classical mechanics. The Lagrange equations allow an exact integration.Tomsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 50–54, November, 1993.     

Spin-1 particle in a homogeneous magnetic field

The Corben-Schwinger theory gives imaginary values of the energy, forS ₃ ² =1 states, in very intensive magnetic fields. The theory proposed by the author, which is most satisfactory in the nonrelativistic approximation, does not have this defect forS ₃ ² =1 states, but it appears forS ₃ ² =0 states.     

Propagator for a charged particle in a time-dependent electromagnetic field

We first show that the propagator of a charged particle in a time-dependent electromagnetic field, obtained by choosing the vector and scalar potentials to be in static symmetric gauge, is related to the propagator of a one-dimensional particle under a time-dependent perturbative force and with generalized memory. For the case of a constant magnetic field, the latter can then be evaluated exactly with the help of a gaussian integral. Our new results are in agreement with the well-known results of simpler cases.     

Wigner functions of a particle in a time-dependent uniform field

Wigner functions and exact transition amplitudes between energy eigenstates for a particle moving in a time-dependent uniform field are calculated.     

Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

Relativistic field formulation of simultaneous quantum measurement

The simultaneous measurement of Dirac field operators is formulated in analogy to the work of von Neumann and Arthurs-Kelly. Meter fields are coupled to the system field with a relativistically invariant bilinear interaction. Measurement of vacuum meter field expectation values provides for the simultaneous measurement of noncommuting system components. It is shown that two meter coupling allows for a simultaneous minimum in the variance of the subsequent meter measurements. A pseudoscalar self-interaction of the Dirac field is shown to allow simultaneous measurement of positive energy field operators with negative energy meters. The simultaneous measurement ofn noncommuting field operators is obtained by coupling the system ton fermionic fields. Also, in this paper the related concept of mutual simultaneous measurement is developed. This requires that any operators in the enlarged Hilbert space are measurable by the remaining fields as meters. System embedding into a larger Hilbert space results in added noise due to the zero point motion of the meter fields. By the negentropy principle of Brillouin, the added noise is equivalent to entropy. A criterion determining the interaction among fields is that the averaged added noise in the components of each quantum field is minimized. This criterion defines an optimum fermionic mass matrix through the determination of the entangling interaction.1. This work was sponsored by the Department of the Air Force under contract F19628-90-C-0002.     

Wigner elementary particle in an external homogeneous field

A covariant Hamiltonian is proposed which permits to describe in the Heisenberg picture the motion of a Wigner elementary particle in a homogeneous electromagnetic field. More precisely, at any time, the elementary particle is in a state associated with a given irreducible representation of the Poincaré group. As a remarkable result, the spin motion is shown to be governed by the Thomas-Bargmann-Michel-Telegdi equation. Also the Galilean limit is discussed.     

Relativistic particle in a three-dimensional box

We generalize the work of Alberto, Fiolhais and Gil and solve the problem of a Dirac particle confined in a 3-dimensional box. The non-relativistic and ultra-relativistic limits are considered and it is shown that the size of the box determines how relativistic the low-lying states are. The consequences for the density of states of a relativistic fermion gas are briefly discussed.     

Relativistic quantum field theory with fractional spin and statistics

We construct a relativistic quantum field theory in 2 + 1 dimensions whose Fock states provide a multivalued representation of the Poincaré group. We add a topological term to the action of a scalar field theory and we show that this endows the path integral of the theory with an operator-valued cocycle which modifies the transformation properties of physical states. We demonstrate that one-particle states carry (in general) fractional spin. We determine the spin of many-particle states and we prove a generalized spin-statistics relation. We propose an equation of motion for on-shell states which generalizes naturally the Dirac equation.