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 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.

Temporally ordered graphs and bound state equations

1955 ◽  
Vol 51 (4) ◽  
pp. 762-765
Author(s):  
J. C. Polkinghorne
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
State Equations ◽  
Single Time ◽  
Ordered Graphs

ABSTRACTOrdered graphs are used to obtain the kernels of the single-time, three dimensional, equations for bound states given by Lévy and Klein, and by Tamm and Dancoff.

THE MASSLESS BOUND STATE FORMALISM IN TWO-PARTICLE RELATIVISTIC QUANTUM MECHANICS

1988 ◽  
Vol 03 (05) ◽  
pp. 1235-1261 ◽  
Author(s):  
H. SAZDJIAN
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Bound State ◽  
Relativistic Quantum Mechanics ◽  
Composite Systems ◽  
Bound State Case ◽  
State Case

We develop, in the framework of two-particle relativistic quantum mechanics, the formalism needed to describe massless bound state systems and their internal dynamics. It turns out that the dynamics here is two-dimensional, besides the contribution of the spin degrees of freedom, provided by the two space-like transverse components of the relative coordinate four-vector, decomposed in an appropriate light cone basis. This is in contrast with the massive bound state case, where the dynamics is three-dimensional. We also construct the scalar product of the theory. We apply this formalism to several types of composite systems, involving spin-0 bosons and/or spin-1/2 fermions, which produce massless 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.

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.

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.

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 Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

Numerical Simulations of Electric Field Driven Self-Assembly of Monolayers of Mixtures of Nanoparticles

2017 ◽  
Author(s):  
E. Amah ◽  
N. Musunuri ◽  
Ian S. Fischer ◽  
Pushpendra Singh
Keyword(s):  
Electric Field ◽  
Physical Properties ◽  
Numerical Simulations ◽  
Self Assembly ◽  
Composite Particle ◽  
Critical Value ◽  
Direct Numerical Simulations ◽  
Composite Particles ◽  
Liquid Interfaces ◽  
Induced Dipole

We numerically study the process of self-assembly of particle mixtures on fluid-liquid interfaces when an electric field is applied in the direction normal to the interface. The force law for the dependence of the electric field induced dipole-dipole and capillary forces on the distance between the particles and their physical properties obtained in an earlier study by performing direct numerical simulations is used for conducting simulations. The inter-particle forces cause mixtures of nanoparticles to self-assemble into molecular-like hierarchical arrangements consisting of composite particles which are organized in a pattern. However, there is a critical electric intensity value below which particles move under the influence of Brownian forces and do not self-assemble. Above the critical value, when the particles sizes differed by a factor of two or more, the composite particle has a larger particle at its core and several smaller particles forming a ring around it. Approximately same sized particles, when their concentrations are approximately equal, form binary particles or chains (analogous to polymeric molecules) in which positively and negatively polarized particles alternate, but when their concentrations differ the particles whose concentration is larger form rings around the particles with smaller concentration.

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