In search of evolution equations in quantum and statistical field theory

Abstract

Using an enlarged space of n-point functions F and fictitious time s linear problems are reformulated in quantum and statistical field theory in such a way that non-negative sesquilinear forms play a crucial role in the description of system. First- and second-order ‘‘evolution’’ type equations are considered and their connection with weak and strong convergence is shown. Supersymmetrical ‘‘evolution’’ of systems is presented without increasing the number of fields. The five-dimensional field theory was found to be useful in developing the formalism.