The Dyson-Schwinger equations give a well-defined tower of linked equations, defining one method of dealing with complex field equations associated with a particular interaction in a particular theory. Usually they are so difficult to solve, that the series of linked equations is truncated at a very low level. Is this a good thing? And do such truncations work for non-Hermitian theories? In this project, we examine these questions and provide some tantalizing answers.
One possible indicator of the physical need for non-Hermitian field theories may occur in the thermal behavior of such theories. We are investigating this for different fermionic and bosonic theories.
