Complexified Path Integrals and the Phases of Quantum Field Theory

Understand

The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle.

• In fact these equations have a multitude of additional solutions which are described by integrals over a complexified path.
• We discuss properties of the additional solutions which, although generally disregarded, may be physical with known examples including spontaneous symmetry breaking and theta vacua.
• We show that a consideration of the full set of solutions yields a description of phase transitions in quantum field theories which complements the usual description in terms of the accumulation of Lee-Yang zeroes.