HET seminar: Keiichi Nagao

Speaker: Keiichi Nagao

Title:  Reality and hermiticity from maximixing overlap in the future-included
complex action theory

Abstract:  In the complex action theory whose path runs over not only past but also future we study a normalized matrix element of an operator O in terms of the future state at the latest time T_B and the past state at the earliest time T_A with a proper inner product which makes a non-normal Hamiltonian at first given normal. We present a theorem which states that provided that the operator O is Q-Hermitian, i.e. Hermitian with regard to the proper inner product the normalized matrix element becomes real and time-develops under a Q-Hermitian Hamiltonian for the past and future states selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. Furthermore, we give a possible procedure to formulate the Q-Hermitian Hamiltonian in terms of Q-Hermitian coordinate and momentum operators, and construct a conserved probability current density. This talk is based on the collaboration with Holger Bech Nielsen. Ref:Prog Theor Exp Phys (2015) 051B01(arXiv:1502.00385[quant-ph])