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

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.

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.

Eigenvalue Equations with Dressed Propagators in a Pole Regularized Spinor Theory

1974 ◽  
Vol 29 (7) ◽  
pp. 991-1002
Author(s):  
K. Dammeier
Keyword(s):  
Binding Energy ◽  
Green’S Function ◽  
Green's Function ◽  
Coupling Constant ◽  
Fermion Propagator ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Small Binding Energy

The massless Green's function in a pole regularized nonlinear spinor theory is dressed and the resulting eigenvalue equations are discussed. The coupling constant is more than doubled by this dressing, and the boson solutions change drastically. The old solutions disappear, a singlett deuteron solution with small binding energy appears. The fermion propagator is determined from a selfconsistency requirement.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

scholarly journals Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Kun-Wen Wen ◽  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Third Order ◽  
Order Nonlinear Differential Equation ◽  
Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

scholarly journals Existence and Lyapunov Stability of Positive Periodic Solutions for a Third-Order Neutral Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng ◽  
Yueli Chen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Lyapunov Stability ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Positive Periodic Solutions ◽  
Third Order

By applying Green's function of third-order differential equation and a fixed point theorem in cones, we obtain some sufficient conditions for existence, nonexistence, multiplicity, and Lyapunov stability of positive periodic solutions for a third-order neutral differential equation.

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