TITLE:
Quantized Field Theory of Fuzzy Space
AUTHORS:
Aleksey M. Avdeenko
KEYWORDS:
Fuzzy Sets, Fuzzy Space, Green’s Function, Regularization, Fuzzy Causality, Gravity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.10,
October
28,
2021
ABSTRACT: The proposed work handles the concept of fuzzy space as a set of real numbers with a set finite membership function. Extending standard arithmetic operations through a fuzzy space, the fuzzy Green’s function is created here with an analysis of its behavior inside and outside the light cone. The fuzzy causality principle is generalized to field models. Also, this work demonstrates the ability to use fuzzy space to regularize divergences in quantum field theory. The passage to the limit to a system of interacting particles enables the obtaining of the dissipative projection operator, represented earlier. The Liouville equation is solved here by successive approximations in the range of times much larger than the typical scale of fuzziness, by assuming the interaction as a small parameter. As well, here was applied the standard diagram technique.