2017/10/05 by Keiichi Nagao, Holger Bech Nielsen, Nagao, Keiichi +2
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.1710.02071
Latex 16 pages, to appear in the proceedings of the 20th workshop "What Comes Beyond the Standard Models", Bled, Slovenia, Jul.9-17, 2017
arxiv created 2017/10/05 · arxiv updated 2017/10/06
In the future-included complex and real action theories whose paths run over not only the past but also the future, we briefly review the theorem on the normalized matrix element of an operator \cal O, which is defined in terms of the future and past states with a proper inner product IQ that makes a given Hamiltonian normal. The theorem states that, provided that the operator \cal O is Q-Hermitian, i.e. Hermitian with regard to the proper inner product IQ, 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. Discussing what the theorem implicates, we speculate that the future-included complex action theory would be the most elegant quantum theory.