Quantization of nonlocal fields via fractional calculus

Abstract

In this study, we investigate the effect of nonlocality in quantum mechanics and propose a fractional approach the theory of quantized fields. For this purpose, we embedded the fractional calculus to broaden theory of quantum fields since the integral and derivative operators are nonlocal in fractional calculus.Additionally, quantum entanglement is discussed to gain comprehension of nonlocality in the foundation of quantum mechanics. Besides, fractional Lagrangian formalism was presented due to fact that the Lagrangian density is the starting point to establish a field theory.Furthermore, to make fractional field operators quantum mechanical, equal-time commutator have been defined for the these operators in terms of Caputo fractional derivative. Thus, a scheme of quantization of fractional fields is introduced and general aspects of the method is illustrated with the theory of massive scalar fields. This approach laid out to a successful generalization of the quantum field theory which is coherent with the standard formalism. Consequently, we developed promising concept for a quantum field theory by introducing nonlocality into standard mathematical formalism.

General Fractional Noether Theorem and Non-Holonomic Action Principle

“…(B1) A fractional action principle and fractional Euler-Lagrange equations are proposed in [51,[75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91]. (B2) A fractional action principle for fractional field theories is considered in [92][93][94][95][96][97][98][99]. (B3) Noether's theory for classical non-conservative mechanics is discussed in [55][56][57].…”