Regular Series


Vol. 10 (1979), No. 11, pp. 945 – 1005


Remarks Concerning the Geometry of Null Strings

abstract

The geometry of totally null complex 2-surfaces (null strings) in a complex space-time is considered. Some theorems concerning the relationship between algebraic types of the energy-momentum tensor and the existence of null strings in the complex space-time are given.


The Perturbed Sine–Gordon Equation

abstract

We discuss some solvable modifications (perturbations) of the sine-Gordon equation which may be modelled by circular pendula in an outer field. The existence and shape, stability and mass formulae for solitons are illustrated by a double-sine-Gordon. A new class of so-called Jacobi–Gordon equations is introduced.


A Non-Compact Gauge Group for the Dirac Equation

abstract

It is shown that infinitesimal transformations of a Dirac spinor, in which small amounts of negative energy states are mixed with positive energy states, together with infinitesimal phase transformations, form the generators of an sl(2,R)-algebra. The global invariance of the Dirac equation obtained in this way is extended to a local invariance by introducing, in addition to the electromagnetic potential, another complex potential, which carries negative energy and is doubly charged. The field equations for the Dirac field coupled to the new gauge fields are derived and a number of special solutions are given.


Larmor Symmetry of Quantum Theory of Massless Vector Field

abstract

Internal symmetries of the two-potential theory of electromagnetic field are considered. It is shown that the group of internal symmetries is O\((3)\otimes \)U(1)\(\otimes \)U(1). Physical interpretation of the related conservation laws is given.


On Fermionic Green’s Function and Fermionic Determinant in Massless QCD\(_2\)

abstract

Exact fermionic Green’s function in massless QCD\(_2\) is obtained by introducing generalized gauge transformations. An explicit, compact expression for the causal fermionic Green’s function is given provided that the gauge potentials satisfy certain conditions. The functional determinant arising from functional integration over the fermionic fields is calculated. The results are expressed in terms of path ordered exponentials.


Fermi Model Description of High Multiplicity Compound Nucleus Decay

abstract

Calculations are performed in the terms of the Fermi model (the model of simultaneous decay) of the emission frequency and velocity distributions of particles with atomic number \(Z \geq 2\), emitted from a highly excited heavy nucleus. The theoretical results are compared with the experimental data obtained from proton—nucleus interactions at 25 GeV/\(c\) and 9 GeV, registered in nuclear emulsions.


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