Almost zerodimensional PTsymmetric quantum field theories
Abstract
In 1992 Bender, Boettcher, and Lipatov proposed in two papers a new and unusual nonperturbative calculational tool in quantum field theory. The objective was to expand the Green's functions of the quantum field theory as Taylor series in powers of the spacetime dimension D. In particular, the vacuum energy for a massless \phi^{2N} (N=1,2,3,...) quantum field theory was studied. The first two Taylor coefficients in this dimensional expansion were calculated {\it exactly} and a set of graphical rules were devised that could be used to calculate approximately the higher coefficients in the series. This approach is mathematically valid and gives accurate results, but it has not been actively pursued and investigated. Subsequently, in 1998 Bender and Boettcher discovered that PTsymmetric quantummechanical Hamiltonians of the form H=p^2+x^2(ix)^\epsilon, where \epsilon\geq0, have real spectra. These new kinds of complex nonDiracHermitian Hamiltonians define physically acceptable quantummechanical theories. This result in quantum mechanics suggests that the corresponding nonDiracHermitian Ddimensional \phi^2(i\phi)^\epsilon quantum field theories might also have real spectra. To examine this hypothesis, we return to the technique devised in 1992 and in this paper we calculate the first two coefficients in the dimensional expansion of the groundstate energy of this complex nonDiracHermitian quantum field theory. We show that to first order in this dimensional approximation the groundstate energy is indeed real for \epsilon\geq0.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 arXiv:
 arXiv:1003.3881
 Bibcode:
 2010arXiv1003.3881B
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 8 pages, 1 figure