Conjugate spinor field equation for massless spin-3/2 field in de Sitter ambient space

The quantum field theory in de Sitter ambient space provide us with a comprehensive description of massless gravitational field. Using the gauge-covariant derivative in the de Sitter ambient space, the gauge invariant Lagrangian density has been found.In this paper, the equation of the conjugate spinor for massless spin-$\frac{3}{2}$ field is obtained by Euler-Lagrange equation. Then the field equation is written in terms of the Casimir operator of the de Sitter group. Finally, the gauge invariant field equation is presented.

Numeric Solutions of Dirac–Gursey Spinor Field Equation Under External Gaussian White Noise

In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.

ABELIAN GAUGE THEORY IN DE SITTER SPACE

Quantization of spinor and vector free fields in four-dimensional de Sitter spacetime, in the ambient space notation, has been studied in the previous works. Various two-point functions for the above fields are presented in this paper. The interaction between the spinor field and the vector field is then studied by the Abelian gauge theory. The U (1) gauge invariant spinor field equation is obtained in a coordinate independent way notation and their corresponding conserved currents are computed. The solution of the field equation is obtained by the use of the perturbation method in terms of the Green's function. The null curvature limit is discussed in the final stage.

On the Connection of Nonrenormalizable and Renormalizable Unified Nonlinear Spinor Field IVfodels

The nonrenormalizable first order derivative nonlinear spinor field equation with scalar interaction possesses two equivalent Hamiltonians. The first is the conventional one while the second is a two-field Hamiltonian with the original field and its parity transform. By quantization the latter leads to an inequivalent representation compared with the former. This is connected with parity symmetry breaking and the loss of simultaneous diagonalization of energy and subfield particle numbers. The corresponding grand canonical Hamiltonian is shown to result equivalently from a renormalizable second order derivative nonlinear spinor field equation. This is achieved by means of a theorem about the decomposition of higher order derivative nonlinear spinor field equations derived previously

Functional Quantum Theory of Scattering Processes. IV

Dynamics of quantum field theory can be formulated by functional equations. To develop a complete functional quantum theory the physical information has to be given by functional operations only. The most important physical information of elementary particle physics is the S-matrix. In this paper the functional ^-matrix is constructed for the scattering of relativistic dressed particles, i.e. for particles with structural properties. The basic functional equation is assumed to be derived from a nonlinear spinor field equation with noncanonical relativistic Heisenberg quantization. The initial free dressed many particle states are defined, and the scattering functionals are constructed. By the use of irreducible representations the equivalence of the functional S-matrix with the conventional Hilbert space definition is shown with respect to an appropriate definition of the functional scalar product. Technical details are discussed in the appendices.