On the Calculation of Vector Mesons in Functional Nonlinear Spinor Theory

1972 ◽  
Vol 27 (11) ◽  
pp. 1539-1553
Author(s):  
W. Bauhoff ◽  
K. Scheerer
Keyword(s):  
Angular Momentum ◽  
Functional Space ◽  
Eigenvalue Equation ◽  
Vector Mesons ◽  
Correct Order ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Calculated Mass ◽  
Order Of Magnitude ◽  
Physical Particle

Abstract Nonlinear spinor theory is fomulated in functional space. An eigenvalue equation for mesons is derived. The group theoretical reduction of this equation is performed, especially the angular momentum decomposition. For vector mesons it is solved in first Fredholm approximation. A solu-tion corresponding to a physical particle is found contrary to earlier calculations. The calculated mass has the correct order of magnitude.

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.

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.

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

Calculations of Eigenvalues in Functional Nonlinear Spinor Theory

1972 ◽  
Vol 27 (7) ◽  
pp. 1042-1057
Author(s):  
K Dammeier
Keyword(s):  
Differential Equation ◽  
Functional Integration ◽  
Eigenvalue Equation ◽  
Fermion Propagator ◽  
Nonlinear Spinor ◽  
Third Order ◽  
Spinor Theory ◽  
Self Consistent ◽  
Integration Techniques ◽  
Modified Theory

Abstract A differential equation of third order for spinor potentials is proposed, that modifies the dynamics of the nonlinear spinor theory. We derive a symmetrical eigenvalue equation using functional integration techniques. This equation and a momentum symmetrized equation - a simplified form of the mass eigenvalue equation proposed by Stumpf - are applied to calculate mass eigenvalues. By a special combination of both methods it is possible to weaken the regulari-zation dipole in Heisenberg's theory and thereby produce better boson masses. Finally, the modified theory allows a self-consistent calculation of the fermion propagator

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.

COSMIC ORIGIN OF QUANTIZATION

2004 ◽  
Vol 18 (04n05) ◽  
pp. 519-525 ◽  
Author(s):  
FRANCESCO CALOGERO
Keyword(s):  
Angular Momentum ◽  
Spatial Coherence ◽  
Simplified Model ◽  
Nucleon Mass ◽  
Universal Gravitation ◽  
Large Component ◽  
Missing Mass ◽  
Order Of Magnitude ◽  
The Universe ◽  
Cosmic Origin

An estimate is presented of the angular momentum associated with the stochastic cosmic tremor, which has been hypothesized to be caused by universal gravitation and by the granularity of matter, and to be itself the cause of quantization ("cosmic origin of quantization"). If that universal tremor has the spatial coherence which is instrumental in order that the estimated action associated with it have the order of magnitude of Planck's constant h, then the estimated order of magnitude of the angular momentum associated with it also has the same value. We moreover indicate how these findings (originally based on a simplified model of the Universe, as being made up only of particles having the nucleon mass) are affected (in fact, essentially unaffected) by the possible presence in the mass of the Universe of a large component made up of particles much lighter than nucleons ("dark", or "missing", mass).

scholarly journals The Near-Synchronous Polar Candidate V4633 Sgr (Nova Sagittarii 1998)

2004 ◽  
Vol 190 ◽  
pp. 176-177
Author(s):  
Y. Lipkin ◽  
E. M. Leibowitz
Keyword(s):  
Angular Momentum ◽  
Momentum Transfer ◽  
White Dwarf ◽  
Moment Of Inertia ◽  
The Other ◽  
Angular Momentum Transfer ◽  
Classical Nova ◽  
Order Of Magnitude ◽  
Photometric Monitoring ◽  
The Moment

AbstractThe classical nova V4633 Sgr (1998) exhibits two photometric periodicities. The shorter period (P1=3.01 hr) is stable, while the other one, longer by ~2.5%, has decreased monotonically since shortly after the nova eruption, with Ṗ2 ≈ –10−6 (Lipkin et al. 2001).Here we report on results of photometric monitoring of the star in 2001 and 2002. During our observations, the longer period decreased more, and in 2002 it was only 1.8% longer than P1 The decrease rate (Ṗ2) in 2001-2002 was an order of magnitude smaller than in 1998-2000.These new results support the Near-Synchronous Polar classification which was suggested for V4633 Sgr (Lipkin et al. 2001). In this model, the longer period of V4633 Sgr is the spin of the white dwarf, and its variation since 1998 reflects changes in the moment of inertia of the white dwarf, and angular momentum transfer in the system following the nova eruption.

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.

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