Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework

DIEGO JULIO CIRILO

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS

SPRINGER/PLENUM PUBLISHERS

Lugar: New York; Año: 2015

0020-7748

Starting from a Unified Field Theory (UFT) proposed previously by the author,the possible fermionic representations arising from the same spacetime are considered fromthe algebraic and geometrical viewpoint. We specifically demonstrate in this UFT generalcontext that the underlying basis of the single geometrical structure P(G,M) (the principalfiber bundle over the real spacetime manifold M with structural group G) reflectingthe symmetries of the different fields carry naturally a biquaternionic structure instead ofa complex one. This fact allows us to analyze algebraically and to interpret physically in astraighforward way the Majorana and Dirac representations and the relation of such structureswith the spacetime signature and non-hermitian (CP) dynamic operators. Also, fromthe underlying structure of the tangent space, the existence of hidden (super) symmetriesand the possibility of supersymmetric extensions of these UFT models are given showingthat Rothstein?s theorem is incomplete for that description. The importance of the Cliffordalgebras in the description of all symmetries, mainly the interaction of gravity with the otherfields, is briefly discussed.