arXiv subjects

Joseph Saaty

Publications and source records attributed to Joseph Saaty.

3 recordsLinked to original sources

arXiv2001

Differential Geometrical Methods for Deriving Dirac's Equation in Curved Spacetime to Account for the Presence of Matter

Differential geomtrical methods for deriving the Dirac equation in Curved Spacetime are presented. Einstein's field equation is applied in a novel manner; in the most current standard reference, Birrell and Davies, 1994 [1], the suggestions for deriving the Dirac equation in Curved Spacetime make no mention of employing Einstein's field equation. Thus, to date, the literature on the derivation of the Dirac equation could not include an expression for the presence of matter. This lack is consistent with earlier publications, including Lichnerowicz's well-known 1964 journal article [3], which presented the first such derivation, and Dimock's 1982 article [2]. The new differential geometrical methods go beyond all previous suggestions, which only apply to cases in the absence of matter. These differential geometrical methods have resulted in derivations of the Dirac equation in Curved Spacetime that apply to either the presence or absence of matter.

math-ph↗

arXiv2001

Nontopological Methods for Determining Topological Charge for Bosons and Fermions in Flat Spacetime

An alternative method to the topological instanton solution for deriving an expression for the topological charge is presented. This alternative method involves the use of relativistic quantum field theory and covariant electrodynamics. In the case of bosons, this method is consistent with the instanton solution in predicting that topological charge is quantized. But furthermore, this method led to the new results that topological charge for fermions cannot be quantized, whereas the instanton solution cannot distinguish between bosons (quantized) and fermions (not quantized). Thus the new technique produced results that were previously unobtainable. Mathematics Subject Classifications (1991): // Key words: Topological charge, Dirac quantization condition, Klein-Gordon equation

math-ph↗

arXiv2001

Topological Charge in Curved Spacetime

This paper presents the extension from flat spacetime into curved spacetime of the area of theoretical investigation that has been known as topological gauge field theory. The extension here presented is based upon a new derivation of the expression for topological charge for bosons and fermions in flat spacetime, a derivation which has been presented elsewhere [1]. This new approach was developed because the established instanton solution could not be extended to curved spacetime. The new approach can be extended to curved spacetime by coupling the major equations of relativistic quantum mechanics to the scalar curvature. The coupling here presented, and results obtained about the quantization of topological charge, had not been possible with the earlier established instanton solution.

math-ph↗