Internal Dynamic Variable Research Articles

Kernel of the classicalZitterbewegung

Barut's classicalzitterbewegung model includes the internal dynamical variables and the quantization of this system gives a general transition amplitude between the different space-time points and internal coordinates and momentum. It includes the transition amplitude between the half integer and integer spin eigenvalues. Spin eigenfunctions lead to all sets of relativistic wave equations, as well as the Dirac equation.

Bi-Local Model with Additional Internal Dynamical Variables and Interaction with External Fields

An extended bi-local model of hadrons is studied based on the picture in which the constituent particles have internal dynamical variables. In particular, we discuss an interaction between the bi-local model and an external scalar field and derive a form factor that is acceptable for the phenomenology. We also calculate a second order scattering amplitude, which shows a good high-energy behavior.

Bi-Local Model with Additional Internal Dynamical Variables and Interaction with External Fields

Bi-Local Model with Additional Internal Dynamical Variables and Interaction with External Fields

Relativistic center-of-mass variables and the harmonic oscillator quark model calculation of the nucleon magnetic moment and the axial-vector coupling constant

We study the introduction of the internal dynamical variables for constituent quarks. These variables are related to the center-of-mass of a nucleon. The problem is connected with the description of spinorial properties of the quarks. The spinors must be artificially introduced in a harmonic oscillator (HO) model. Experimental values of the magnetic moment and the axial-vector coupling constant of a nucleon can be easily reproduced. The theoretical results are not sensitive to the theoretical details; they follow from the general properties of the quark structure of baryons. The connections with the relativistic HO models are also discussed. The case of a very small confinement radius is explored in the Appendix.

Dirac positive-energy wave equation with para-Bose internal variables

Dirac's new infinite-component positive-energy relativistic wave equation is generalized by introducing para-Bose internal dynamical variables. Electromagnetic interaction of Dirac's particle is studied and the origin of the difficulty in the original formulation identified. It is seen to be evaded by our generalization, a special case of which for para-Bose variables of order 2 is discussed elsewhere. Our equation also describes a spinless positive-energy unique-mass particle in the absence of external fields. We outline the new Dirac theory in 1 + 1 and 2 + 1 dimensions.

Electromagnetic interactions of weakly-bound composite systems

Relativistic definitions of c.m. and internal dynamical variables are obtained for a weakly bound, Lorentz invariant system containing an arbitrary number of particles. The method used is a generalization of the one developed by Osborn for the case of two-body systems. Once defined, the variables are used in a study of the interaction of composite systems with an external electromagnetic field. It is found that one obtains additional relativistic corrections to those usually included in such calculations. These corrections can be classified as being either spin dependent or spin independent. The importance of the former has previously been established. The importance of the latter is established here. Finally, it is shown that the Drell-Hearn Gerasimov sum rule can now be validated for an arbitrary, weakly-bound N-body system.

Lorentz Commutators of Internal Dynamical Variables

A definition of internal dynamical variables which includes the unitary-spin generators is used to determine the pure Lorentz commutators of these variables in the presence of nonconserving interactions. A geometrical interpretation of the nonvanishing Lorentz commutators is presented in terms of the hyperplane formalism, previously discussed by the author.