Carl M. Bender, V. Branchina, Emanuele Messina
It was shown recently that a PT-symmetric \(i\phi^3\) quantum field theory in \(6-\epsilon\) dimensions possesses a nontrivial fixed point. The critical behavior of this theory around the fixed point is examined and it is shown that the corresponding phase transition is related to the existence of a nontrivial solution of the gap equation. The theory is studied first in the mean-field approximation and the critical exponents are calculated. Then, it is examined beyond the mean-field approximation by using renormalization-group techniques, and the critical exponents for \(6-\epsilon\) dimensions are calculated to order \(\epsilon\). It is shown that because of its stability the PT-symmetric \(i\phi^3\) theory has a higher predictive power than the conventional \(\phi^3\) theory. A comparison of the \(i\phi^3\) model with the Lee-Yang model is given.
http://arxiv.org/abs/1301.6207
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Carl M. Bender, V. Branchina, Emanuele Messina
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric ig\phi^3 quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p^2+ix^3, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization-group properties of a conventional Hermitian g\phi^3 quantum field theory with those of the PT-symmetric ig\phi^3 quantum field theory. It is shown that while the conventional g\phi^3 theory in d=6 dimensions is asymptotically free, the ig\phi^3 theory is like a g\phi^4 theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
http://arxiv.org/abs/1201.1244
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)