Hamiltonian Flow Equations for a Dirac Particle in an External Potential

We derive and solve the Hamiltonian flow equations for a Dirac particle in an external static potential. The method shows a general procedure for the set up of continuous unitary transformations to reduce the Hamiltonian to a quasidiagonal form.Comment: 6 page

Electromagnetic wave scattering by many small particles

Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear algebraic system have physical meaning. They are expressed in terms of the electric and magnetic polarizability tensors. Analytical formulas are given for calculation of these tensors with any desired accuracy for homogeneous bodies of arbitrary shapes. An idea to create a "smart" material by embedding many small particles in a given region is formulated

Wave scattering by small particles in a medium

Wave scattering is considered in a medium in which many small particles are embedded. Equations for the effective field in the medium are derived when the number of particles tends to infinity

Spin and Rotation in General Relativity

Rapporteur's Introduction to the GT8 session of the Ninth Marcel Grossmann Meeting (Rome, 2000); to appear in the Proceedings.Comment: LaTeX file, no figures, 15 page

Physical Consequences of Anomalies in Nonlocal Potential Problems

An s-wave two-body separable potential may give rise to several phenomena which are absent for nonsingular local potentials. We examine the physical implications of a well known example of such phenomena, the continuum bound state, as well as of two lesser known anomalies, the so-called positive energy spurious state and negative energy bound states with improper long-range behavior. By examining these anomalies in light of Levinson\u27s theorem, Wigner\u27s phase shift inequality, and the effect of a perturbation on the anomalous states by their insertion in a three-body scattering situation, we find in agreement with previous studies that the continuum bound state acts as a resonance of negligible width. However, we find it difficult to see how the presence of a spurious state can be detected experimentally

The Phenornenological Theory of Exchange Currents in Nuclei

As was first pointed out by Siegert, the existence of exchange forces in nuclei implies the existence of accompanying exchange currents. Sachs has calculated an expression for these, by making the Hamiltonian containing exchange potentials gauge-invariant, and has applied it to the calculations of exchange magnetic moments in H3 and He3. The Hamiltonian obtained by Sachs is not the most general admissible one. More generally, the exchange current density is found to depend on a vector function whose irrotational part is completely determined by gauge-invariance but whose solenoidal part is arbitrary except for the requirements (following from conditions of translational invariance and symmetry in all nucleons on the Hamiltonian) that it be translationally invariant and antisymmetric under the exchange of the spin and space coordinates of each pair of nucleons. Making use of these conditions on the Hamiltonian, the explicit form of the dependence of the solenoidal part of the exchange current upon the spin and isotopic spin coordinates of the nucleons has been derived. In the resultant exchange moments, the irrotational part leads to the expression obtained by Sachs, while the solenoidal term contribution contains the spin operators of the nucleons in particular combinations, together with arbitrary functions of the nucleon separation. Villars' exchange moment expression, as obtained from meson theory, is included as a special case and hence the exchange contributions to the moments of H3 and He3 are explicable on a phenomenological basis, contrary to the results obtained in Sachs' special case. The generality and significance of the results are discussed in relation to the various meson theories.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86129/1/PhysRev.79.795-RKO.pd

Foldy-Wouthuysen transformation for relativistic particles in external fields

A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed. It permits determination of the Hamilton operator in the Foldy-Wouthuysen representation with any accuracy. Interactions between a particle having an anomalous magnetic moment and nonstationary electromagnetic and electroweak fields are investigated.Comment: 22 page

On a possible approach to the variable-mass problem

The mass operator M is introduced as an independent dynamical variable which is taken as the translation generator P_4 of the inhomogenous De Sitter group. The classification of representations of the algebra P(1,4) of this group is performed and the corresponding P(1,4) invariant equations for variable-mass particles are written out. In this way we have succeeded, in particular, in uniting the ``external'' and ``internal'' (SU_2) symmetries in a non-trivial fashion.Comment: 4 page

Zitterbewegung and reduction: 4D spinning particles and 3D anyons on light-like curves

We construct the model with light-like world-lines for the massive 4D spinning particles and 3D anyons. It is obtained via the formal bosonization of pseudoclassical model for the massive Dirac particle with subsequent reduction to the light-like curves. The peculiarity of the light-like trajectories produced due to the Zitterbewegung is explained from the viewpoint of reduction and reparametrization invariance.Comment: 10 pages, discussion expanded and references added. To appear in Phys. Lett.