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

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 the Functional Definition and Calculation of Global Observables in Nonlinear Spinor Field Quantum Theory

1972 ◽  
Vol 27 (7) ◽  
pp. 1058-1072
Author(s):  
H Stumpf
Keyword(s):  
Quantum Theory ◽  
Spinor Field ◽  
Free Field ◽  
Functional Space ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Spinor Fields

Abstract Nonlinear spinor theory contains unobservable field operators which cannot be identified with free field operators. Therefore for the comparson with experiment a theory of observables for nonlinear spinor fields is required. This theory is developed for global observables by means of a map into functional space, and leads to a functional quantum theory of nonlinear spinor fields

On the Construction of Relativistic Representation Spaces in Functional Quantum Theory of the Nonlinear Spinor Field

1975 ◽  
Vol 30 (11) ◽  
pp. 1361-1371 ◽  
Author(s):  
H. Stumpf ◽  
K. Scheerer
Keyword(s):  
Quantum Theory ◽  
State Space ◽  
Functional State ◽  
Spinor Field ◽  
Function Spaces ◽  
The State ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
State Spaces ◽  
Representation Spaces

Functional quantum theory is defined by an isomorphism of the state space H of a conventional quantum theory into an appropriate functional state space D It is a constructive approach to quantum theory in those cases where the state spaces H of physical eigenstates cannot be calculated explicitly like in nonlinear spinor field quantum theory. For the foundation of functional quantum theory appropriate functional state spaces have to be constructed which have to be representation spaces of the corresponding invariance groups. In this paper, this problem is treated for the spinor field. Using anticommuting source operator, it is shown that the construction problem of these spaces is tightly connected with the construction of appropriate relativistic function spaces. This is discussed in detail and explicit representations of the function spaces are given. Imposing no artificial restrictions it follows that the resulting functional spaces are indefinite. Physically the indefiniteness results from the inclusion of tachyon states. It is reasonable to assume a tight connection of these tachyon states with the ghost states introduced by Heisenberg for the regularization of the nonrenormalizable 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.

Symmetry Conditions on Nonlinear Spinor Field Functionals/The symmetry conditions of nonlinear spinor theory of elementary particles, i.e. the definitions of quantum numbers, are given for the nonlinear spinor field functionals.

1970 ◽  
Vol 25 (11) ◽  
pp. 1556-1561 ◽  
Author(s):  
H. Stumpf ◽  
K. Scheerer ◽  
H.G. Märtl
Keyword(s):  
Quantum Theory ◽  
Spinor Field ◽  
Preceding Paper ◽  
Functional Space ◽  
Invariance Group ◽  
Mathematical Meaning ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Quantum Numbers ◽  
Symmetry Properties

The operator equations of quantum theory can be replaced formally by functional equations of corresponding Schwinger functionals 1-3. To give this formalism a physical and mathematical meaning one has to develop a complete functional quantum theory as has been proposed in a preceding paper4. Then the complete physical information has to be given by functional operations only. Especially the quantum numbers of ordinary quantum theory have to be reproduced functionally. As the quantum numbers are defined by the eigenvalues of the generators of the corresponding invariance groups, one has to investigate these quantities in functional space. This is done in this paper. To have a definite model we consider the nonlinear spinor field with noncanonical relativistic Heisenberg quantization 5 the form invariance group of which is the Poincare group. Although this model has still other symmetry properties we restrict ourselves to the discussion of the quantum number conditions resulting from this group, as the considerations for other groups and models are quite analogous.

scholarly journals Scalarproducts of Spinor Field Functionals and State Representations in Nonlinear Spinor Field Quantum Theory

1975 ◽  
Vol 30 (6-7) ◽  
pp. 708-720
Author(s):  
H. Stumpf
Keyword(s):  
Quantum Theory ◽  
Cross Sections ◽  
Spinor Field ◽  
Field Operator ◽  
Particle Scattering ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Quantum Theories ◽  
General Dynamics ◽  
Scalar Products

Abstract In preceding papers it was shown that in nonlinear spinor theory cross-sections of elementary particle scattering processes can be calculated only if the state representations and their scalar products are explicitly known. To obtain these quantities, functional quantum theory of the non-linear spinor field was introduced-In this paper it is demonstrated that the introduction of functional scalar products in functional quantum theory is equivalent to impose restrictions to the spinor field operator itself concerning its groundstate behaviour. Performing this, explicit state representations of spinor field states as well as corresponding scalar products can be derived, leading thus to functional quantum theories of the spinor field in dependence on the groundstate model. It follows from these considerations that a spinor field quantum theory is in principle in-complete, as long as no additional assumptions on the groundstate are made, which cannot be derived from the general dynamics of the field.

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 Numerical Solution of the Spinor-Spinor Bethe-Salpeter Equation in Functional Nonlinear Spinor Theory

1975 ◽  
Vol 30 (5) ◽  
pp. 656-671
Author(s):  
W. Bauhoff
Keyword(s):  
Angular Momentum ◽  
Excited State ◽  
Variational Method ◽  
Numerical Solution ◽  
High Precision ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
First Order ◽  
Scalar Mesons ◽  
Functional Methods

AbstractThe mass eigenvalue equation for mesons in nonlinear spinor theory is derived by functional methods. In second order it leads to a spinorial Bethe-Salpeter equation. This is solved by a variational method with high precision for arbitrary angular momentum. The results for scalar mesons show a shift of the first order results, obtained earlier. The agreement with experiment is improved thereby. An excited state corresponding to the η' is found. A calculation of a Regge trajectory is included,too.

scholarly journals The Nonrelativistic Scattering States of the Deng-Fan Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Bentol Hoda Yazarloo ◽  
Liangliang Lu ◽  
Guanghui Liu ◽  
Saber Zarrinkamar ◽  
Hassan Hassanabadi
Keyword(s):  
Approximation Scheme ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Term Energy ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Nonrelativistic Scattering

The approximately analytical scattering state solution of the Schrodinger equation is obtained for the Deng-Fan potential by using an approximation scheme to the centrifugal term. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated. We consider and verify two special cases: thel=0and thes-wave Hulthén potential.

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