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.

Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. III

1985 ◽  
Vol 40 (3) ◽  
pp. 294-302
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 dynamic 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.

Effective Interactions of Relativisic Composite Particles in Unified Nonlinear Spinor-Field Models. II

1985 ◽  
Vol 40 (2) ◽  
pp. 183-190 ◽  
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 the Derivation of Strong and Electro-weak Interactions in Functional Quantum Theory of the Nonlinear Spinor Field as a Lepton-hadron Model with Quark-confinement

1981 ◽  
Vol 36 (3) ◽  
pp. 261-271 ◽  
Author(s):  
H. Stumpf
Keyword(s):  
Spinor Field ◽  
Bound States ◽  
Gauge Theories ◽  
Weak Interactions ◽  
Relativistic Quantum ◽  
Strong Interactions ◽  
Quark Confinement ◽  
Nonlinear Spinor ◽  
Calculation Technique ◽  
Non Local

In preceding papers the nonlinear spinor field with Heisenberg's dipole regularization was interpreted as a lepton-quark system. In this paper it is demonstrated that this model is able to produce electro-weak as well as strong interactions. For the analytical derivation of these interactions, in Section 1 an improved calculation technique for scattering functionals is developed which corresponds to an interaction representation of relativistic quantum fields with inclusion of bound states, and which is suited for a comparison of its results with conventional field theories, in particular gauge theories. In Section 2 the projection technique from the spinor field into the lepton-quark representation is discussed in detail. The principle which allows the derivation of the various interactions consists in the calculation and incorporation of universal (local) bosons and non-universal (non-local) bosons occuring as bound states of the spinor field, resp., leptonquark fields, into the scattering functional equation. This is performed for local bosons in Section 1 and for non-local bosons in Section 3. In Section 4 it is shown that a subsequent unitarization which corresponds to quark confinement leads to selection rules for lepton-baryon processes which qualitatively correspond to those of grand unification gauge theories. Numerical calculations will be given in subsequent papers

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

Effective Boson-Fermion Dynamics for Subfermion Models

1994 ◽  
Vol 49 (6) ◽  
pp. 649-662
Author(s):  
G. Grimm
Keyword(s):  
Bound States ◽  
Field Model ◽  
Composite Particle ◽  
Effective Field ◽  
Composite Models Of Particles ◽  
Field Equations ◽  
Nonlinear Spinor ◽  
General Group ◽  
Unified Field ◽  
Composite Models

Abstract Effective composite particle dynamics can be derived by weak mapping of quantum fields. This method was already applied to derive effective boson or boson-fermion coupling theories from a nonlinear subfermion field. In this paper we present an extension of those calculations to the general group theoretical treatm ent of two-fermion bound states and their coupling to (elementary) fermions within an arbitrary nonlinear spinor-isospinor field model. The resulting effective field equations are com pared with the corresponding phenomenological expressions which for example underly the standard electroweak theory. PACS 11 .10 - Field theory.PACS 12.10 - Unified field theories and models. PACS 12.35 - Composite models of particles.

On the Calculation of Nonlinear Spinor Field Functionals. III

1976 ◽  
Vol 31 (6) ◽  
pp. 528-539
Author(s):  
H. Stumpf
Keyword(s):  
Spectral Decomposition ◽  
Spinor Field ◽  
Scattering Theory ◽  
Integration Method ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Scattering States ◽  
Irreducible Part ◽  
Nonrelativistic Scattering ◽  
Inelastic Processes

The limitations of the Green functions method concerning nonlinear spinor theory are discussed. To remove these difficulties, functional quantum theory of the nonlinear spinor field was introduced in preceding papers. To obtain numerical values for the global observables in this theory, the functional eigenstates have to be calculated. In this paper especially for functional scattering states appropriate equations are derived. A general integration method of the spinor field functional equation is introduced, leading to an equation for the irreducible part of the state functional. Generating functionals are defined, allowing a separation of selfenergy and interactionenergy terms in the equation of the irreducible part. By spectral decomposition of the scattering functionals the boundary conditions are examined, which lead in connection with selfenergy and interactionenergy terms to the construction of channel equations for the irreducible part of elastic scattering functionals. The method is extented to inelastic processes, it can be tested in the case of nonrelativistic scattering theory. The procedure for the three particle case is discussed in some details

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.

Exchange Forces of Composite Particles in Quantum Field Theory

1991 ◽  
Vol 46 (5) ◽  
pp. 389-400
Author(s):  
W. Pfister ◽  
H. Stumpf
Keyword(s):  
Functional Equations ◽  
Bound States ◽  
Composite Particle ◽  
Field Evaluation ◽  
Particle Dynamics ◽  
Composite Particles ◽  
Quantum Field ◽  
Composite Boson ◽  
Functional Representation ◽  
Composite Bosons

AbstractQuantum fields can be characterized by state functionals and corresponding functional equations. Within this functional representation exchange forces of composite particles are discussed for the case of composite bosons which are bound states of two constituent fermions. The dynamics of these bosons is formulated by means of a weak mapping theorem which establishes a map between the functional equations for the composite boson quantum field and the constituent original fermion quantum field. Evaluation of this theorem leads to expressions which can be identified as quantum field theoretic "direct" forces and exchange forces for or between composite particles. By some theorems the exchange forces are evaluated and an estimate for them is given. The expressions for the direct forces correspond to those which were already derived in previous papers to discuss composite particle dynamics.

scholarly journals Proof of Renormalizability and Derivation of Dynamical Equations for Relativistic Composite Particle Systems and Reactions in Unified Field Models

1981 ◽  
Vol 36 (12) ◽  
pp. 1289-1298
Author(s):  
H. Stumpf
Keyword(s):  
Bound States ◽  
Composite Particle ◽  
Bound State ◽  
Composite Particles ◽  
State Equations ◽  
Dynamical Equations ◽  
General Reaction ◽  
Composite Systems ◽  
Unified Field ◽  
Reaction Equations

AbstractIn any quantum field theory of matter, in particular in quark-and subquark models, bound states have to be treated. In coupling theories corresponding bound state equations are derived by the Gell-Mann-Low procedure from the Greenfunction hierarchy. Due to certain presupposi-tions neither the derivation of such generalized Bethe-Salpeter equations nor the normalization of their amplitudes are selfconsistent. In this paper bound state equations and general reaction equations for composite particles are derived by means of functional techniques which do not rest on such presuppositions. The derivation is performed for a unified lepton-quark model with boson fusion from fermions, which is described by a nonlinear spinorfield equation with higher order derivatives. Besides the removal of infinities, in coupling theories renormalization mainly means the introduction of dressed field operators which allow a biunique map between field opera-tors and particles. For composite particles renormalization means the dressing of the composite systems which must allow the unique identification of dressed composite particle states independently of the interactions which can take place with other composite systems, i.e. this is in principle the same program as in coupling theories but with the treatment of dressed composite particles instead of dressed field operators. The program is performed for the reaction equations mentioned above.

scholarly journals Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

1985 ◽  
Vol 40 (7) ◽  
pp. 752-773
Author(s):  
H. Stumpf
Keyword(s):  
Composite Particle ◽  
Particle Interaction ◽  
High Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Statistical Interpretation ◽  
Quantum Field ◽  
Mapping Procedure ◽  
Effective Dynamics ◽  
Rough Approximation

Unified nonlinear spinorfield models are self-regularizing 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 and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced 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. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

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