Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-01-05
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, 2 figures
Scientific paper
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.
Bender Carl M.
Branchina Vincenzo
Messina Emanuele
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