Fractional Quantum Field Theory: From Lattice to Continuum

Abstract EN

An approach to formulate fractional field theories on unbounded lattice space-time is suggested.

A fractional-order analog of the lattice quantum field theories is considered.

Lattice analogs of the fractional-order 4-dimensional differential operators are proposed.

We prove that continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum 4-dimensional space-time.

The fractional field equations, which are derived from equations for lattice space-time with long-range properties of power-law type, contain the Riesz type derivatives on noninteger orders with respect to space-time coordinates.