A non-perturbative study of non-hermitian, PT-symmetric cubic scalar quantum field theory

Fueled by a recent conjecture of D. Bessis that non-Hermitian, [special characters omitted] symmetric Hamiltonians have positive and real energies, the study of such theories has recently received much attention. Most of the work has been done in the context of quantum mechanics. Several techniques have been used up to date, including numerical and variational approaches. Field theoretic techniques have also been used, but always applied to one dimensional theories. This class of quantum field theories is isomorphic to quantum mechanics. In this dissertation we present the first study of a non-Hermitian, [special characters omitted] symmetric quantum field theory. We apply the methods of Modal Field Theory and Quasy-sparse Eigenvector Diagonalization to the study of a scalar quantum field theory with a cubic interaction and an imaginary coupling constant. The spectrum is examined and found to be real and positive. The vacuum expectation value of the field is imaginary and shows a peak in the nonperturbative regime. The physical mass is found to increase monotonically with the coupling strength