Selected Publications:Huygens' Principle and the Unification of Dynamics, Proceedings of the Conference on Theoretical Physics, University of Georgia September 12, 1997(George Strobel, editor). In this paper Huygens' Principle in its most general form is used to express the quantum scattering dynamics of an interacting system with an infinite, changing number of degrees of freedom. The results are non perturbative, embodying the principles of proper normalization. A new concept, the relative probability amplitude is introduced to describe intrinsically nonlinear interactions.
Quantum Mechanics and Nonlinear Waves (Harwood Academic Press, N.Y.1981).This monograph describes the research on intrinsically nonlinear quantum field theories, beginning with a re-examination of the fundamental ideas of non interacting theories. The central role of the superposition principle of quantum theory is emphasized in the subsequent analysis of non perturbative, self interacting quantum field theories. The new concept of proper normalization of interacting quantum field theories eliminates the inconsistencies of perturbative renormalization, eliminating the infinities which are common to such theories. An extensive discussion of non perturbative solution of nonlinear field equations includes some of the most important nonlinear field equations occurring in physics. Applications to elementary particle physics, superconductivity and other topics of high current interest form an integral part of the book.
Non perturbative Solution of Nonlinear Field Equations, Nuovo Cimento 100B,43,1987. In this paper a new technique for solving nonlinear ordinary and partial differential equations independent of traditional methods is explored. This technique employs a transformation of second order differential equations to a set first order generalizations of the Riccati equation. Approximations are introduced in these new equations. Applications to the Lane-Emden, nonlinear Klein Gordon and other equations are given.
Boundary Conditions in Quantum Field Theories, Foundations of
Physics 23, 965,1993. From its inception quantum electrodynamics and other
quantum field theories have contained serious inconsistencies. The source
of these inconsistencies has been the assumption that interactions among systems
can develop out of non interacting systems. In this paper quantum
electrodynamics and some other important quantum field theories are shown to be
persistently interacting. The interaction strength must always appear in
the solutions to the field equations.
Some Graduates Of the Program:
Mesgun Sebhatu:Dissertation: "Quantized Solitary Waves in Nonlinear Field Theories and Their Application to Nucleon-Nucleon and Nucleon-Antinucleon Interactions." Presently Professor of Physics, Winthrop University. Internationally recognized for his work in low energy nuclear physics and, in particular, for the development of SWEPs, Solitary Wave Exchange Potentials, Dr. Sebhatu received a King-Parks-Chavez Fellowship for sabbatical research in nuclear physics in 1991-92.
Beverley A.P.Taylor: dissertation;"Solitary Waves in Relativistically Invariant Field Theories and Their Applications to the Electromagnetic Interactions of Hadrons." Presently Professor of Physics, Miami University-Hamilton. Internationally recognized for innovations in physics education, Dr. Taylor was recognized by the American Association of Physics Teachers with its Distinguished Service Citation, 1996.
William Ditto:Dissertation: "A Study of the Properly Normalized Lamb Shift and a New Non perturbative Method of Solution to Nonlinear Field equations Using Continued fractions." Presently Associate Professor of Physics, Georgia Institute of Technology, Dr. Ditto has received significant international recognition for his work in chaos. An excerpt from his research is a feature of the 1998 American Physical Society Calendar.
Julie Talbot: M.S. Thesis,"Variational Calculation of PSWEP parameters," Ph.D. research in progress on the nonperturbative calculation of radiative corrections to the magnetic moments of charged vector mesons.
Some Earlier Work:
Substantial evidence is accumulating for the existence of coherent, spin zero meson excitations. In this note some properties of these excitations are discussed and a comparison of theoretical predictions with recent experiments is given.
Coherent spin zero excitations are described by an intrinsically nonlinear quantum field theory described by the field equation (1,2)
This equation has exact solutions describing coherent quantum fields for (2,3). The interesting case for this note is p=3/2. The propagator for these solutions for this case is (1,2)
where has no poles for k real. The poles of this propagator give the mass formula
when we apply this theory to neutral pions. These are the masses of the excited, coherent states of the system for all positive integers n. In the table, a comparison of the theoretical predictions with recent experimental observations is made (4,5,6).
There are several important points about these excitations which should be emphasized. In the first place, they are non perturbative. The solutions of the field equations are non perturbative, hence the mass spectrum itself is. The spectrum depends only on the exponent in the interaction, not on the coupling constants. This seems to be in good agreement with the experimental results, with perhaps small corrections necessary to improve the fit. Finally, the fact that these are coherent excitations of a single system means that they will appear in virtual processes as a part of the system propagator. The significance of this property is currently being explored in the context of the standard model (7).
1. P. B. Burt, Lett. al Nuovo Cimento 13, 26 (1975).
2. P. B. Burt, "Quantum Mechanics and Nonlinear Waves" (Harwood Academics Press, N.Y. 1981).
3. P. B. Burt, Phys. Rev. Lett. 32, 1080 (1974).
4. European Physical Jour. C3, 1-4 (Tables of Particle Properties 1998).
5. J. Z. Bai et al., Physics Lett. B446, 356 (1999).
*^6. D. V. Bugg, "Workshop on Hadron Spectroscopy '99", Frascati (March 1999) and private communication.
7. P. B. Burt, "Coherent Neutral Pion Excitations in Nucleons" in preparation.
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