Spinor Realization Research Articles

Quantum theory with arrow of time: symmetry breaking and non-local spinor realization with non-commuting operators of energy and decay

We present a modified quantum dynamics with a non-Hermitian Hamiltonian ≠ +, and a complex parameter of evolution. The theory is developed with [+, ] = κ2, where κ is the new fundamental constant. It is shown that this theory loses its symmetry in the case of κ ≠ 0. We demonstrate that this theory allows a thermodynamical interpretation and possesses an 'arrow of time' for isothermal and adiabatic regimes of evolution. A realization of this theory is a modified four-dimensional Dirac spinor system, which appears non-local in the physical three-dimensional space.

Spinor field realizations of non-critical [formula omitted] strings

In this paper, we construct the nilpotent Becchi–Rouet–Stora–Tyutin (BRST) charges of spinor non-critical W 2 , s strings. The cases of s = 3 , 4 are discussed in detail, and spinor realization for s = 4 is given explicitly. The BRST charges are graded.

Coset Constructions of Conformal Blocks

On the basis of the coset construction, we obtained canonical maps that relate the sheaf of conformal blocks of the Wess–Zumino–Witten model to those of the unitarizable Virasoro minimal model. We conjectured that the maps are isomorphisms. Making use of spinor realizations, we confirmed the conjecture for the case of the Ising model. We also discussed the coherency of the sheaf of conformal blocks for the Virasoro algebra.

Coset constructions of conformal blocks

On the basis of the coset construction, we obtained canonical maps that relate the sheaf of conformal blocks of the Wess–Zumino–Witten model to those of the unitarizable Virasoro minimal model. We conjectured that the maps are isomorphisms. Making use of spinor realizations, we confirmed the conjecture for the case of the Ising model. We also discussed the coherency of the sheaf of conformal blocks for the Virasoro algebra.

A geometrical formulation of electrodynamics

A geometrical formulation of electrodynamics is presented. This formulation is based on a nonlinear constraint for the electromagnetic potential. As a consequence of the constraint, a three-dimensional photon field is associated with the co-ordinates of a symmetric space of constant negative curvature. A formalism covariant under general co-ordinate transformations is constructed and extended, in a manner analogous to that used in general relativity, to include spinor realizations. A generally covariant Lagrangian density is exhibited and shown to be equivalent, by a suitable redefinition of the fields, to the usual electrodynamics. In such an approach a close relationship between Lorentz invariance and the electromagnetic interaction is manifest.

New Relativistic Coulomb Hamiltonian with O(4) Symmetry and a Spinor Realization of the Dynamical Group O(4,2)

The Dirac-Coulomb Hamiltonian with a simple modification of the scalar potential corresponding to switching off the interaction of the small components is solved by a new squaring procedure and is shown to describe a system possessing O(4) symmetry. The new realization of the generators of the corresponding O(4,2) dynamical group shows a nontrivial but natural mixing of the space and spin coordinates in which the total angular momentum replaces the usual orbital angular momentum.

Realization of Chiral Symmetry in a Curved Isospin Space

The nonlinear realizations of the chiral group SU(2)⊗SU(2) are studied from a geometric point of view. The three-dimensional nonlinear realization, associated with the pion field, is considered as a group of coordinate transformations in a three-dimensional isospin space of constant curvature, leaving invariant the line element. Spinor realizations in general coordinates are constructed by combined coordinate-spin-space transformations in analogy to Pauli's method for spinors in general relativity. The description of vector mesons and possible chiral-invariant Lagrangians, which yield the various nonlinear models in specific frames of general coordinates, are discussed.