Hidden Symmetry Group Research Articles

The Symmetries and the General Harmonic Solution to Equations of Maxwell Electrodynamics with an Axion

The effective Lagrangian is derived and a group of hidden symmetries is determined for Maxwell’s theory with an axion in the stationary case. The general harmonic solution is constructed, and it is shown that a central source can have only a Coulomb-type magnetic field. The electric field of such a source has a complex potential, which can be finite everywhere with a special choice of parameters. The differential scattering cross section of the test particle on a dione with an axionic charge is calculated within the first order of the perturbation theory.

On the sigma-model structure of type IIA supergravity action in doubled field approach

In this letter, we describe how to string together the doubled field approach by Cremmer, Julia, Lü, and Pope with the Pasti-Sorokin-Tonin technique to construct the sigma-model-like action for type IIA supergravity. The relation of the results with those obtained in the context of searching for superstring/M-theory hidden symmetry group is discussed.

De Sitter quasigroups

The Cayley–Klein parameters for the de Sitter groups SO(4, 1) and SO(3, 2) are introduced, and in an extension of the earlier investigation of quasigroups connected with Clifford groups, quasigroups connected with the SO(4, 1) and SO(3, 2) groups are determined. It is shown that these quasigroups have eight-dimensional, double-valued irreducible cracovian representations. The covariance of a five-dimensional form of the Dirac equation with respect to the quasi-rotations forming quasigroups connected with the groups SO(4, 1) and SO(3, 2) is demonstrated. An analogy is drawn between Weyl's hidden symmetry group and a quasigroup.

NEW PROGRESS IN STATIONARY D=N=4 SUPERGRAVITY

A bosonic sector of the four-dimensional low-energy heterotic string theory with two Abelian gauge fields is considered in the stationary case. A new 4× 4 unitary null-curvature matrix representation of the theory is derived and the corresponding formulation based on the use of a new 2 × 2 Ernst type matrix complex potential is developed. The group of hidden symmetries is described and classified in the matrix-valued quasi general relativity form. A subgroup of charge symmetries is constructed and representation which transforms linearly under the action of this symmetry subgroup is established. Also the solution generation procedure based on the application of the total charge symmetry subgroup to the stationary Einstein–Maxwell theory is analyzed.

Effective QCD chiral lagrangian for pions and vector mesons and hidden local symmetry

Starting from the QCD path integral in the low energy region we derive an effective lagrangian for pions and vector mesons as gauge bosons of the hidden local symmetry. We use two chiral anomalies related to (a) the standard chiral group and current quarks and (b) the hidden symmetry group and constituent quarks. The effective lagrangian depends on one parameter F π , the pion decay constant.

On a hidden symmetry of a relativistic Coulomb problem in the quasipotential approach

The Runge-Lenz vector for a relativistic Coulomb problem in the quasipotential approach is found. The energy spectrum is obtained by an algebraic method. A hidden symmetry group of this problem is shown to be a group O(4) for mod E mod 1 and a motion group of the three-dimensional Euclidean space for mod E mod =1.