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.     

Supersymmetric Dirac particles in Riemann-Cartan space-time

A natural extension of the supersymmetric model of Di Vecchia and Ravndal yields a nontrivial coupling of classical spinning particles to torsion in a Riemann-Cartan geometry. The equations of motion implied by this model coincide with a consistent classical limit of the Heisenberg equations derived from the minimally coupled Dirac equation. Conversely, the latter equation is shown to arise from canonical quantization of the classical system. The Heisenberg equations are obtained exact in all powers of and thus complete the partial results of previous WKB calculations. We touch also on such matters of principle as the mathematical realization of anticommuting variables, the physical interpretation of supersymmetry transformations, and the effective variability of rest mass.     

Pseudoscalar and pseudovector coupling of a pion to a bound Dirac nucleon

The non-equivalence of pseudoscalar and pseudovector coupling of a pion to a Dirac nucleon in the presence of a scalar-vector potential is analysed and found to be strongly related to the magnitude of spin-orbit splitting. The concept of a Galilean invariant vertex operator turns out to be unjustified for a bound nucleon.     

Two-dimensional radiative transfer due to curved Dirac delta line sources

In this article, the two-dimensional radiative transport equation is considered for the curved Dirac delta line source. In order to account this source type, Green’s function of the radiative transport equation for the half-plane is derived in parts of the ballistic and diffuse contribution as well as under consideration of the Fresnel reflection at the boundary. The final results are verified with the Monte Carlo method for different collimated beams and several curved sources such as the elliptic and logarithmic spiral line source.     

Hawking radiation of Dirac particles in Kasner-type spacetime

The Hawking radiation of Dirac particles is studied in Kasner-type spacetime. Its anisotropy gives rise to particle creation.     

Center-of-mass motion of a system of relativistic Dirac particles

The relativistic center-of-mass motion for a system ofN fermions can be exactly separated because of the linearity of the Dirac operators in momenta which is not possible for quadratic Klein-Gordon particles. The covariant equations derived from Maxwell-Dirac field theory are considered. The center-of-mass equation is still a 4 ^N -component spinor equation. We solve these equations for two- and three-body systems, as well as the relative motion for the non-interacting case, and discuss the quantum numbers and identification of eigenstates and eigenvalues. The results apply for both bound and scattering states. Dedicated to the Third Centenary of the Publication of Principia: Corollary IV.... and therefore the common center of gravity of all bodies acting upon each other (excluding external actions and impediments) is either at rest, or moves uniformly in a right line. Is. Newton, Philosophiae Naturalis Principia Mathematica (S. Pepys, Julii 5, 1686, Londini)     

Levinson theorem for Dirac particles in one dimension

The scattering of Dirac particles by symmetric potentials in one dimension is studied. A Levinson theorem is established. By this theorem, the number of bound states with even(odd)-parity, n₊ (n_-), is related to the phase shifts [] of scattering states with the same parity at zero momentum as follows: The theorem is verified by several simple examples. Received 26 August 1998 and Received in final form 18 January 1999     

Energy levels of the hydrogen atom due to a generalized Dirac equation

The consequences of a generalized Dirac equation are discussed for the energy levels of the hydrogen atom. Apart from the usual generalizations of the Dirac equation by adding new interaction terms, we generalize the anticommutation rule of the Dirac matrices, which leads to spin-dependent propagation properties. Such a theory can be looked at as a model theory for testing Lorentz invariance or as an outcome of pregeometric dynamical induction schemes for space-time structure.For special examples of generalized Dirac matrices including perturbation terms with respect to the SRT Dirac matrices, we derive the energy level of the hydrogen atom and find a hyperfine splitting due to these perturbations. A comparison of this additional splitting with Lamb shift measurements gives us upper limits for possible perturbations, which turn out to be of measurable magnitude. Spin precession experiments give much more restrictive limits. So, it turns out that the hydrogen atom is not such a sensitive indicator for the Lorentz invariance as widely believed.     

Generalized phase factors and the interaction of Dirac particles

The nonintegrable phase factor approach to interactions is generalized in the case of a Dirac particle. The results differ significantly from those obtained in the Schrödinger theory and allow Dirac particles to be characterized by two fundamental couplings.     

Stationary bound states of Dirac particles in collapsar fields

It is the first time stationary bound states of elementary spin 1/2 particles that do not decay with time are obtained for a Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product in a wide range of gravitational coupling constant. In order to obtain a discrete energy spectrum, we introduce a boundary condition such that the current density of Dirac particles near the “event horizon” is zero.     

Alternative approaches to the construction of the Poincare-invariant spin operators of the Dirac particles

At present a number of methods of constructing the Poincare-invariant spin operators for relativistic particles with half-integer spin in the one-particle theory are well known. The method of odd operator constructing, the Lorentz method of bilinear covariant form transformation, and the method with the Foldy–Wouthuysen representation belong to them. New approaches to the construction of spin operators are developed in the present work, namely, a method of separating space-like component directly from the spin matrices of bilinear covariant forms, including the method of multiplication of the covariant Hamiltonian of the Dirac equation by these matrices. By this means we succeeded in constructing the Poincare-invariant spin operators by simpler and mathematically faultless methods. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 10–15, November, 2008.     

Losses in pendular suspensions due to centrifugal coupling

We present an analysis of the centrifugal coupling of a simple pendulum to a dissipative support. We show that such a coupling leads to an amplitude dependent quality factor. For amplitudes which could be present in laser interferometer gravitational wave detector suspensions, this mechanism could limit the quality factor of the test mass suspension significantly to 10¹⁰ and should be considered in the design of advanced LIGO type detectors.     

Instabilities due to charge-density-curvature coupling in charged membranes

Instabilities are caused by the reduction in the electrostatic energy when the membrane is curved with the higher charge density on the bilayer which is stretched by the curvature. In a bilayer where the charges can flip from one lipid layer to the other, there is a thermodynamic instability to a spontaneously curved state with different charge densities on the two sides. If the charges are not permitted to flip, there is a dynamical instability due to the correlated modulation of the charge density and curvature fields. Numerical estimates show that these effects are present in parameter regimes relevant to biological systems.     

Quadrupole coupling in EuO due to lattice imperfections

From ¹⁵³Eu nuclear spin-spin relaxation measurements it is concluded that quadrupole effects observed in ferromagnetic EuO are due to lattice imperfections.