# The Basic Problems of Nonlocal Quantum Field Theory

Chapter

## Abstract

In this chapter we present the main ideas of constructing the nonlocal theory of quantized fields. Our basic postulation states that in quantum field theory nonlocality arising from the stochastic nature of space-time is manifested only in interaction processes between fields. In other words, it means that we must introduce nonlocality into the interaction Lagrangians of different fields. This proposal has some basis. Indeed, if we maintain the Einstein relation between momentum and energy

*E*= (**p**^{2}+*m*^{2})^{1/2}to be valid for extended fields constructed by means of the relativistic invariant distributions \( K({{l}^{2}}\square ) \) (*l*^{2}□) (1.11), then they will satisfy free field equations, for example, in the case of the one-component scalar field*φ*_{ R }(*x*) =*φ*(*x*):$$
(\square - {{m}^{2}})\phi (x) = 0. $$

(2.1)

## Keywords

Green Function Wave Packet Scalar Particle Causality Condition Imaginary Time
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## Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1986