Solution of Schwinger-Dyson equations for PT-symmetric quantum field theory -: art. no. 085001

In recent papers it has been observed that non-Hermitian Hamiltonians, such as those describing ig phi (3) and -g phi (4) field theories, still possess real positive spectra so long as the weaker condition of PT symmetry holds. This allows for the possibility of new kinds of quantum field theories that have strange and quite unexpected properties. In this paper a technique based on truncating the Schwinger-Dyson equations is presented for renormalizing and solving such field theories. Using this technique if is argued that a -g phi (4) scalar quantum field theory in four-dimensional space-time is renormalizable, is asymptotically free, has a nonzero value of [0\phi \0], and has a positive definite spectrum. Such a theory might be useful in describing the Higgs boson.