scholarly journals Nonlinear Spinor Field Equations in Gravitational Theory: Spherical Symmetric Soliton-Like Solutions

2012 ◽  
Vol 03 (09) ◽  
pp. 935-942 ◽  
Author(s):  
V. Adanhounme ◽  
A. Adomou ◽  
F. P. Codo ◽  
M. N. Hounkonnou
Keyword(s):  
Spinor Field ◽  
Gravitational Theory ◽  
Field Equations ◽  
Nonlinear Spinor ◽  
Symmetric Soliton

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

1984 ◽  
Vol 39 (5) ◽  
pp. 441-446
Author(s):  
H. Stumpf
Keyword(s):  
Field Equation ◽  
Spinor Field ◽  
Order Derivative ◽  
Simultaneous Diagonalization ◽  
Field Equations ◽  
Nonlinear Spinor ◽  
Original Field ◽  
Higher Order Derivative ◽  
Grand Canonical ◽  
Spinor Field Equation

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

Discussion of the Two-Fermion Sector in a Unified Nonlinear Spinor Field Model with Indefinite Metric II

1983 ◽  
Vol 38 (11) ◽  
pp. 1184-1188
Author(s):  
H. Stumpf
Keyword(s):  
State Space ◽  
Spinor Field ◽  
Bound States ◽  
Direct Calculation ◽  
Indefinite Metric ◽  
Relativistic Energy ◽  
Field Equations ◽  
Nonlinear Spinor ◽  
Unified Field ◽  
Fermion Fields

In unified field models all observable (elementary and nonelementary) particles are assumed to be bound states of elementary unobservable fermion fields. Such models are formulated by selfregularizing higher order nonlinear spinor field equations with indefinite metric. The latter needs a careful investigation of the corresponding state space, in particular with respect to bound states. Based on preceding papers the general analysis of the state space is further developed in the framework of a relativistic energy representation in Part I. In Part II this formalism is applied to bound states of the two-fermion sector for a simple model. By direct calculation it turns out that for very heavy masses of the constituent fields bound states with positive norm and small masses are possible, i.e., that the two-fermion sector allows a meaningful physical interpretation

Discussion of the Two-Fermion Sector in a Unified Nonlinear Spinor Field Model with Indefinite Metric I

1983 ◽  
Vol 38 (10) ◽  
pp. 1064-1071 ◽  
Author(s):  
H. Stumpf
Keyword(s):  
State Space ◽  
Spinor Field ◽  
Bound States ◽  
Direct Calculation ◽  
Indefinite Metric ◽  
Relativistic Energy ◽  
Field Equations ◽  
Nonlinear Spinor ◽  
Unified Field ◽  
Fermion Fields

Abstract In unified field models all observable (elementary and non-elementary) particles are assumed to be bound states of elementary unobservable fermion fields. Such models are formulated by self-regularizing higher order nonlinear spinor field equations with indefinite metric. The latter needs a careful investigation of the corresponding state space, in particular with respect to bound states. Based on preceding papers the general analysis of the state space is further developed in the framework of a relativistic energy representation in Part I. In Part II this formalism is applied to bound states of the two-fermion sector for a simple model. By direct calculation it turns out that for very heavy masses of the constituent fields bound states with positive norm and small masses are possible, i.e., that the two-fermion sector allows a meaningful physical interpretation.

scholarly journals Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. I

1985 ◽  
Vol 40 (1) ◽  
pp. 14-28
Author(s):  
H. Stumpf
Keyword(s):  
Spinor Field ◽  
Bound States ◽  
Composite Particle ◽  
Composite Particles ◽  
Statistical Interpretation ◽  
Particle Spectrum ◽  
Nonlinear Spinor ◽  
Effective Interactions ◽  
Scattering States ◽  
Diagonal Part

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

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