COMPLEXIFIED FRACTIONAL HEAT KERNEL AND PHYSICS BEYOND THE SPECTRAL TRIPLET ACTION IN NONCOMMUTATIVE GEOMETRY

Abstract

From points of view of physics, fractional operators represent a vital role for describing intermediate processes and critical phenomena in physics. Subsequently, fractional Action-Like Variational Approach in the sense of Riemann–Liouville fractional integral has lately gained significance in exploring nonconservative dynamical systems found in classical and quantum field theories. Within the same framework, fractional Dirac operators are introduced and the fractional spectral action principle is constructed and some interesting consequences are discussed. In particular, we show that the fractional spectral triplet action is complexified and the disturbing huge cosmological term may be eliminated. The generalization of the problem in view of the generalized fractional integration operators, namely the Erdélyi–Kober fractional integral is also discussed.