On the nonlinear spinor theory of elementary particles

1972 ◽  
Vol 5 (18) ◽  
pp. 1129-1132 ◽  
Author(s):  
A. I. Naumov
Keyword(s):  
Elementary Particles ◽  
Nonlinear Spinor ◽  
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 ON POSSIBLE GEOMETRIC AND ASTROPHYSICAL EFFECTS OF NONLINEAR SPINOR FIELDS IN THE MEGAMIR, MACROWORLD AND MICROWORLD

Metaphysics ◽  
2020 ◽  
pp. 82-93
Author(s):  
V. G Krechet
Keyword(s):  
General Relativity ◽  
Gravitational Interaction ◽  
Space Time ◽  
Elementary Particles ◽  
Nonlinear Spinor ◽  
Evolution Of The Universe ◽  
Spinor Fields ◽  
Astrophysical Objects ◽  
Local Space ◽  
The Universe

In this article, within the framework of general relativity, the possible effect of the gravitational interaction of Dirac nonlinear spinor fields on the evolution of the Universe, on the formation of astrophysical objects and on the formation of the geometry of the local space-time of elementary particles with spin ħ / 2 is considered.

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 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

Zur Berechnung der Masse des Fermions in einer nichtlinearen Spinortheorie

1961 ◽  
Vol 16 (3) ◽  
pp. 225-227
Author(s):  
Keyword(s):  
Density Function ◽  
Particle State ◽  
Present Calculation ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Zero Mass ◽  
Contraction Function ◽  
Normal Particle

The contraction function 〈0 | T ψα(x) ψ̅β(x′) |0〉 occurring in the nonlinear spinor-theory of HEISENBERG has been approximated by assuming that the density function ρ (ζ) contains a normal particle state at ζ=ϰ2 and α dipoleghost at ζ= m2. This assumption is slightly more general than that in the original paper where the mass of the dipoleghost was taken as ζ=0. The intention of the present calculation was to see whether the approximaion could be improved in this way and whether a certain inconsistency mentioned in the earlier paper would disappear. The nucleon massvalue xN l is calculated in the lowest approximation of the new TAMM-DANCOFF method. It is shown that only for m2/ϰ2 less than about 0.05 real values of ϰN l are obtained, i. e. the dipoleghost has to be assumed at zero mass or very near to it. The inconsistency of the method mentioned in earlier work still persists.

The mass eigenvalue problem for baryons in the nonlinear spinor theory

1968 ◽  
Vol 54 (3) ◽  
pp. 639-694 ◽  
Author(s):  
H. P. Dürr ◽  
F. Wagner
Keyword(s):  
Eigenvalue Problem ◽  
Nonlinear Spinor ◽  
Spinor Theory

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

Zur Zweipunktfunktion in nichtlinearen Spinortheorien

1960 ◽  
Vol 15 (9) ◽  
pp. 753-758 ◽  
Author(s):  
H. Mitter
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Rest Mass ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Propagation Function ◽  
General Physical

The propagation function of a nonlinear spinor theory with γ5-invariance is studied in an approximation which neglects four-point- and higher correlations. The resulting nonlinear differential equation is solved. The only solution fulfilling certain general physical requirements (microcausality, positive energies) corresponds to a “dipole ghost” of zero rest mass.

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