A relation between the dirac field of the electron and electromagnetic fields

There is a point of view from which a field governed by the Dirac equation for the electron is the same as a field governed by the Maxwell-Lorentz equations for electromagnetic fields. This observation suggests the possibility that the two sets of equations are of the same origin.     

New twistorial integral formulas for massless free fields of arbitrary spin

A manifestly scaling-invariant version of the Kirchoff-D'Adhemar-Penrose field integrals is presented. The invariant integral expressions for the spinning massless free fields are directly transcribed into the framework of twistor theory. It is then shown that the resulting twistorial field integrals can be thought of as being equivalent to the universal Penrose contour integral formulas for these fields.     

Energy spectrum of the dirac equation for the Scharzschild and Kerr fields

We consider the effect of relativistic corrections and rotation of the central body on the structure of the energy spectrum of a particle with spin in the Schwarzchild and Kerr fields. A splitting of levels is obtained, which corresponds to the classical shift of the perihelion of the orbit and precession of the plane of the gravitational spin-orbit interaction and several nonlinear spin effects are calculated.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 2, pp. 86–92, February, 1988.     

Real complexified quantum groups,their vector fields and quantum enveloping algebras

We construct complex quantum groups associated with the Lie algebras of typeA _n–1 ,B _n ,C _n andD _n which are considered as real algebras. Following the ideas of Faddeev, Reshetikhin and Takhtayan, we obtain the Hopf algebras of regular functionalsU _R , on these real complexified quantum groups. Theq-analogues of the left invariant vector fields of the quantum enveloping algebras are defined. These quantum vector fields are functionals over the corresponding real formA of the complex quantum groupA. The equivalence of the Hopf algebra of regular functionals and the algebra of complex quantum vector fields is shown by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals. In the special exampleA ₁ , we derive theq-deformed real complexified enveloping algebraU _q sl(2, ) with six generators.Presented at the Colloquium on the Quantum Groups, Prague, 18–20 June, 1992.Based on the papers: [i]Drabant B., Schlieker M., Weich W., and Zumino B.: PreprintLMU-TPW 1991-5 (to appear in Commun. Math. Phys.) [ii]Chryssomalakos C., Drabant B., Schlieker M., Weich W., and Zumino B.: Preprint UCB 92/03 (to appear in Commun. Math. Phys.) [iii]Drabant B., Juro B., Schlieker M., Weich W., and Zumino B.: Preprint MPI-Ph/92-39 (submitted to Lett. Math. Phys.)     

Existence of standing waves for dirac fields with singular nonlinearities

We prove the existence of stationary states for nonlinear Dirac equations of the form (E) $$i\sum\limits_{\mu = 0}^3 {\gamma ^\mu \partial _\mu \psi - M\psi + F\left( {\bar \psi \psi } \right)\psi = 0,} $$ whereM>0 andF is a singular self-interaction. In particular, in the model case whereF(s)=?s ^?α, for some 0<α<1, and for every ω>M, there exists a solution of (E) of the form ψ(t, x)=e ^iωt?(x), wherex ₀=t andx=(x ₁,x ₂,x ₃), such that ? has compact support. IF 0<α<1/3, then ? is of classC ¹. If 1/3<α<1, then ? is continuously differentiable, except on some sphere {|x|=R}, where |??| is infinite.     

Foldy-Wouthyusen transformation and exact description of spin dynamics in strong external fields

The most common form of optoacoustic generation is thermoelasticity. Thermoelastic transduction is easy to implement and can be very broadband. However, its major drawback has always been poor conversion efficiency when a metallic film is used as the transducer. We have investigated two alternate structures for high efficiency, one based on a thin polymer film and the other using a two-dimensional nanostructure.     

Reflection,transmission and spin rotation of dirac neutrinos in magnetic fields

Reflection and transmission coefficients of Dirac neutrinos with a magnetic moment through magnetic fields are calculated. The motion is in three dimensions. We find that one spin component can undergo a total reflection, but the other not, this effect being most pronounced at neutrino energies equal to the magnetic energyμB. We also determine the spin rotation angle (equivalently the helicity rotation angle).     

Group-theoretic description of external gauge fields

For an arbitrary external gauge field we construct an infinite group which contains all the information about the given field and describes some of its properties. We construct a field representation of the group . We show that covariant derivatives become translation generators in such a representation of the group . This allows us to interpret transformations from the group as motions in an external gauge field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 31–35, December, 1988.     

Microscopic shell-model description of the irrotational-flow dynamics

The European Physical Journal A - We reconsider the chiral Lagrangian with three-flavor baryon fields. A systematic analysis of all low-energy constants (LEC) that contribute to the axial-vector...     

Hamiltonian description of bubble dynamics

The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.     

A rational interpretation of the dirac equation for the electron

Rationalization of the interpretation of the Dirac equation for the electron lies beyond the conventional scope of quantum mechanics. This difficulty motivates a revision of the system of quantum mechanics through which the indeterministic trait is eliminated from the system.