Zitterbewegung of particles with arbitrary spin

The existence of zitterbewegung of particles with higher spins (s≥1) is proved. The investigation is based on the idea of Curie, Jordan, and Sudarshan that there are two aspects of relativistic invariance and also on the determination of the dynamical variables that describe systems with arbitrary spin obtained by Jordan and Mukunda. A number of new paradoxical properties of zitterbewegung unknown in Dirac theory is revealed. For example, particles with high spins (s≥1) can have a velocity greater than light. It is shown in a general form that elimination of zitterbewegung in all directions of space, or even only in a plane, is impossible. There can be only partial liquidation of zitterbewegung, in one of the directions of space, and then only at the price of violation of relativistic invariance of the theory. Finally, it is suggested that the paradoxical properties of zitterbewegung can be understood by redefining the momentum and mass operators. In this way, a connection between zitterbewgung and tachyons is established.     

Quadrupole and contact interaction of relativistic particles with the electric field of crystals

The Hamiltonian for the quadrupole and the contact interaction of relativistic particles with an electrostatic field is found. The equation of motion for the particle spin is derived.     

Clustering of Fermi particles with arbitrary spin

A single l-shell model is investigated for a system of fermions of spin s and an attractive s-wave, spin channel independent, interaction. The spectra and eigenvectors are determined exactly for different l,s values and particle numbers N. As a generalization of Cooper pairing it is shown that when N=mu(2s+1), mu=1,2,..., 2l+1, the ground state consists of clusters of (2s+1) particles. The relevance of the results for more general situations including the homogeneous system is briefly discussed.     

Interacting Bhabha field with arbitrary spin

The Bhabha equation which describes a particle having multi-mass and spin states with maximum spin S, integer or half an odd integer, is considered. In the presence of interactions e.g. the electromagnetic interaction introduced through minimal coupling, it is found to yield the same (anti-) commutators as in the case of a free field. Also the propagation of an interacting field is causal. This shows the absence of inconsistencies of the type, pointed out by Johnson and Sudarshan. Finally the applicability of the methods of quantisation is discussed.     

Repolarization of atomic muons by polarized nuclei of arbitrary spin

Repolarization of the muon in the 1S atomic state by the hyperfine interaction with the polarized and oriented nucleus of arbitrary spin is discussed by determining the time dependence of the vector polarizations.     

Relativistic polarization density matrix for particles of arbitrary spin

The polarization density matrix for particles of arbitrary spin can be expressed as a linear function of the expectation values of the generators of the polarization symmetry group of the corresponding wave equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–88, April, 1984.     

Conformal invariance of relativistic equations for arbitrary spin particles

We show that any Poincaré-invariant equation for particles of zero mass and of discrete spin provide a unitary representation of the conformal group, and find an explicit expression of the conformal group generators in terms of Poincaré group generators.     

Calculation of the number density of particles produced by a variable electric field during an arbitrary time

A calculation is made of the number density n of quasiparticles determined by the condition of diagonality of the Hamiltonian of a quantized field in a nonstationary external electric field. It is shown that for finite t the number n contains terms that describe real produced particles, vacuum polarization, and interference between the polarization and production effects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 52–56, January, 1981.I thank A. A. Grib and V. M. Mostepanenko for helpful discussions.     

Motion of dirac particles possessing an anomalous magnetic moment in a centrally symmetric electric field

States of a relativistic electron having an anomalous magnetic moment and moving in a centrally symmetric field are classified by a method most similar to a nonrelativistic classification. A spin quantum number is clearly defined. The motion of a neutron in a central field is also investigated. Some new, exact solutions of the Dirac-Pauli equation are found. A classical interpretation of the results is conducted.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 38–45, November, 1971.     

带电粒子在地磁场中的运动

用计算机模拟的方法研究了地磁场中带电粒子的运动特性,绘制了粒子轨迹曲线,对粒子运动进行了分析,解释了地磁场的磁瓶效应和辐射带.     

Motion of test particles in a torsion field

The solution of the Mathisson-Papapetrou equations generalized to the case of the Einstein-Cartan theory, when they describe the motion of a test particle in an external torsion field, is considered. It is shown that a particle of nonzero rest mass moves inertially in a constant polarized torsion field, but its spin precesses around the direction of polarization of the spin of the torsion source. It is also found that the motion of a massless particle in a variable torsion field leads to a torsion frequency displacement effect of a photon under the assumption that the photon spin interacts with the torsion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 84–87, August, 1980.     

Two particle unitarity for helicity amplitudes with particles of arbitrary spin

The two particle unitarity contribution to the double spectral function of the scattering amplitude for any 2 → 2 process is explicitly calculated for the case of arbitrary spins of the initial, intermediate and final particles. A closed, simple result is obtained which is a generalization of the Mandelstam result for spinless particles. The results should be of value in calculations of the contribution of the exchange of pairs of high spin particles to the nucleon-nucleon force.     

Effective operators of the spin correlated crystalline electric field

The effective operators of the spin correlated crystal field have been formed by coupling the exchange with the crystal field. The exchange field is a scalar in spin space so the effective operators will still have the same rank as that of the crystal field but will give non-zero matrix elements between the states ^2S+1L_J of the half filled shells, contrary to the zero value obtained for a pure crystal field tensor.     

Long time evolution of a spin interacting with a spin bath in arbitrary magnetic field

We introduce a completely different method to calculate the evolution of a spin interacting with a sufficient large spin bath,especially suitable for treating the central spin model in a quantum dot(QD).With only an approximation on the envelope of central spin,the symmetry can be exploited to reduce a huge Hilbert space which cannot be calculated with computers to many small ones which can be solved exactly.This method can be used to calculate spin-bath evolution for a spin bath containing many(say,1000)spins,without a perturbative limit such as strong magnetic field condition,and works for long-time regime with sufficient accuracy.As the spin-bath evolution can be calculated for a wide range of time and magnetic field,an optimal dynamic of spin flip-flop can be found,and more sophisticated approaches to achieve extremely high polarization of nuclear spins in a QD could be developed.     

Kerr-de Sitter黑洞任意自旋粒子的隧穿辐射及其熵修正

运用超越半经典近似理论研究了Kerr-deSitter黑洞事件视界处的任意自旋粒子的隧穿辐射,并得到了修正的Hawking温度和粒子隧穿率.利用修正的Hawking温度和迹反常理论,进一步得到了此黑洞的修正熵,结果表明,超越半经典近似理论可适用于各种自旋粒子的隧穿辐射.     

Lattice sum of electric field gradients in tetragonal crystals

A new method to calculate the lattice contribution to electric field gradients at a nuclear site in tetragonal crystals is developed. The crystal is regarded as an assembly of positive ions at lattice points embedded in a uniform background of negative charge (point charge model). The method uses Euler-Maclaurin formula and makes the plane-wise summation in the direct crystal space unlike most of the previous methods utilising Fourier transform to reciprocal space. The numerical values obtained using the above approach agree well with previous results.     

On the propagation of solutions for the wave equations describing the particles with arbitrary spin

The casual propagation of Hurley wave equations for a massive particle with an arbitrary spin s, interacting minimally with an external electromagnetic field, is found to be due to the nature of the β-matrices satisfying Harish Chandra's condition analogous to the spin-one case.