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.

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

On the Calculation of Nonlinear Spinor Field Functionals. II

1974 ◽  
Vol 29 (4) ◽  
pp. 549-555
Author(s):  
H. Stumpf
Keyword(s):  
Quantum Theory ◽  
Calculation Method ◽  
Spinor Field ◽  
Preceding Paper ◽  
Bound State ◽  
High Energy ◽  
The State ◽  
Nonlinear Spinor ◽  
Scattering State

In preceding papers a functional quantum theory has been developped. In this theory the physical observables are derived only by functional operations from the corresponding state functionals. To obtain physical informations therefore the state functionals have to be known and calculational procedures have to be developped. As high energy phenomena are of interest the state functionals of the nonlinear spinor field are considered. In a preceding paper I a calculation method for bound state functionals has been proposed. In this paper this method is extended to the calculation of scattering state functionals, resulting in channel equations for the various scattering processes in the dynamics of the nonlinear spinor field.

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.

Nucleon-Nucleon Scattering Calculations in a Pole Regularized Spinor Theory

1974 ◽  
Vol 29 (7) ◽  
pp. 981-990
Author(s):  
K. Dammeier
Keyword(s):  
Quantum Theory ◽  
Cross Section ◽  
Test Object ◽  
Nucleon Nucleon ◽  
Coupling Constant ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Order Of Magnitude ◽  
The Right ◽  
Right Order

A pole regularized nonlinear spinor theory may be a suitable test object to compare scattering calculations of Stumpf's functional quantum theory with LSZ-results. To apply the LSZ-technique in this theory, a dressing of the occurring massless Green's function is necessary. It is shown which special approximations allow for this dressing. The renormalized nucleon-nucleon coupling constant yields the right order of magnitude for the elastic nucleon cross section.

On the Calculation of Nonlinear Spinor Field Functionals

1971 ◽  
Vol 26 (4) ◽  
pp. 623-630 ◽  
Author(s):  
H Stumpf
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Spinor Field ◽  
Functional Equations ◽  
High Energy ◽  
Quantum Field ◽  
Nonlinear Spinor ◽  
Physical Problems ◽  
Physical Information

Abstract Dynamics of quantum field theory can be formulated by functional equations. To develop a complete functional quantum theory one has to describe the physical information by functional operations only. Such operations have been defined in preceding papers. To apply these operations to physical problems, the corresponding functionals have to be known. Therefore in this paper calculational procedures for functionals are discussed. As high energy phenomena are of interest, the calculational procedures are given for spinor field functionals. Especially a method for the calculation of stationary and Fermion-Fermion scattering functionals is proposed.

On the Evaluation of Scalarproducts of Nonlinear Spinorfield State Functionals

1981 ◽  
Vol 36 (10) ◽  
pp. 1024-1031
Author(s):  
H. Stumpf
Keyword(s):  
Quantum Theory ◽  
State Space ◽  
Quark Model ◽  
A Priori ◽  
Preceding Paper ◽  
Functional Space ◽  
Nonlinear Field ◽  
Metrical Structure ◽  
Metric Tensor ◽  
Linear State

The metrical structure of the linear state space of a quantized nonlinear field cannot be given a priori. Rather it is determined by the dynamics of the field itself. For the evaluation of state norms and scalarproducts this metric must be known. In functional quantum theory the metrical structure is expressed by the metric tensor G (j) in functional space. Equivalent to the knowledge of G (j) is the knowledge of the set of dual state functionals {|S(j, a)〉} together with the corre-sponding original state functionals {|F(j, a)〉} . In preceding papers attempts were made to calculate G (j). In this paper an approach is made to determine the dual state functionals directly. Equations are derived which have to be satisfied by the dual functionals. The method works in those state sectors which are characterized by real (monopole) particles or monopole ghosts, while it does not work for multipole ghost states. Norm calculations are performed for local monopole fermion states and local monopole boson states of the lepton-quark model derived in a preceding paper.

scholarly journals On the Normalization of Meson Eigenstates in Functional Quantum Theory of the Nonlinear Spinor Field

1974 ◽  
Vol 29 (3) ◽  
pp. 376-384
Author(s):  
D. Englert ◽  
H. Stumpf
Keyword(s):  
Functional Equation ◽  
Quantum Theory ◽  
Spinor Field ◽  
Negative Parity ◽  
Positive Definite ◽  
Positive Parity ◽  
Nonlinear Spinor ◽  
Scalar Mesons ◽  
Meson States

In the framework of the functional quantum theory of the nonlinear spinor field the normalization of functional eigenstates of scalar mesons is performed. By calculating the lowest approximation of the functional eigenstates for scalar mesons from the dynamical functional equation of the theory, it follows that scalar mesons of positive as well as of negative parity are admitted. Requiring a positive norm for physical particles the result of normalization shows that mesons with positive parity are excluded, while meson states with negative parity give a positive definite norm. This corresponds to experimental experience

On the Calculation of Scalar Mesons in Functional Nonlinear Spinor Theory

1974 ◽  
Vol 29 (10) ◽  
pp. 1394-1406
Author(s):  
W. Bauhoff
Keyword(s):  
Integral Equation ◽  
Angular Momentum ◽  
Scalar Meson ◽  
Functional Space ◽  
Order Equation ◽  
Second Order ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
First Order ◽  
Scalar Mesons

Abstract The formulation of nonlinear spinor theory in functional space is used for the calculation of scalar meson masses. The second order equation used, requires an explicit angular momentum reduction. For illustration, this method is also applied to the first order equation. In second order, we get an integral equation of the Bethe-Salpeter type which is solved in Fredholm approximation.

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

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