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 posses s real positive spectra so long as the weaker condition of PT symmetry hold s. This allows for the possibility of new kinds of quantum field theories t hat have strange and quite unexpected properties. In this paper a technique based on truncating the Schwinger-Dyson equations is presented for renorma lizing and solving such field theories. Using this technique if is argued t hat 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.