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.

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

Composite Gluons and Effective Nonabelian Gluon Dynamics in a Unified Spinor-Isospinor Preon Field Model

1987 ◽  
Vol 42 (3) ◽  
pp. 213-226 ◽  
Author(s):  
H. Stumpf
Keyword(s):  
Field Equation ◽  
Field Model ◽  
Bound State ◽  
Composite Models Of Particles ◽  
Gauge Bosons ◽  
Effective Interactions ◽  
Unified Field ◽  
Effective Dynamics ◽  
Composite Models ◽  
Composite Gluons

The model is defined by a selfregularizing nonlinear preon field equation and all observable (elementary and non-elementary) particles are assumed to be bound (quantum) states of the fermionic preon fields. In particular electroweak gauge bosons are two-particle composites, leptons and quarks are three-particle composites, and gluons are six-particle composites. Electroweak gauge bosons, leptons and quarks and their effective interactions etc. were studied in preceding papers. In this paper gluons and their effective dynamics are discussed. Due to the complications of a six-particle bound state dynamics the formation of gluons is performed in two steps: First the effective dynamics of three-particle composites (quarks) is derived, and secondly gluons are fusioned from two quarks respectively. The resulting effective gluon dynamics is a non-abelian SU(3) dynamics, i.e. this local gauge dynamics is produced by the properties of the composites and need not be introduced in the original preon field equation. Mathematically these results are achieved by the application of functional quantum theory to the model under consideration and subsequent evaluation of weak mapping procedures, both introduced in preceding papers. PACS 11.10 Field theory. PACS 12.10 Unified field theories and models. PACS 12.35 Composite models of particles.

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.

scholarly journals A Method of Calculating Bound States in a Unified Field Model

1983 ◽  
Vol 38 (10) ◽  
pp. 1056-1063
Author(s):  
D. Großer ◽  
B. Hailer ◽  
L. Hornung ◽  
T. Lauxmann ◽  
H. Stumpf
Keyword(s):  
Hilbert Space ◽  
Kinetic Energy ◽  
Bound States ◽  
Field Model ◽  
Elementary Particles ◽  
Unified Field ◽  
Explicit Representations ◽  
Space Vectors ◽  
The Masses ◽  
Derivatives Of

Abstract In a model in which the usual elementary particles (leptons, quarks, photons, weak bosons, gluons, and so on) are bound states of truly elementary fermions we present a method for the calculation of the masses of these bound states. The kinetic energy of this model contains derivatives of second order so that the four-fermion interaction becomes renormalizable. The method uses explicit representations for the Hilbert space vectors of bound states.

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.

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.

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.

scholarly journals Effective field equations and scale-dependent couplings in gravity

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
Alfio Bonanno ◽  
Georgios Kofinas ◽  
Vasilios Zarikas
Keyword(s):  
Effective Field ◽  
Field Equations

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

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