2012/01/05 by Carl M. Bender, Vincenzo Branchina, V. Branchina +1
Mathematics · Physics and Astronomy · #Combinatorics #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Mathematical physics #Mathematics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Topological Materials and Phenomena #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevd.85.085001
13 pages, 2 figures
arxiv created 2012/01/05 · openalex publication_date 2012/04/02 · arxiv updated 2013/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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\ensuremathφ3 quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p2+ix3, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian g\ensuremathφ3 quantum field theory with those of the PT-symmetric ig\ensuremathφ3 quantum field theory. It is shown that while the conventional g\ensuremathφ3 theory in d=6 dimensions is asymptotically free, the ig\ensuremathφ3 theory is like a g\ensuremathφ4 theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.