Reality from maximizing overlap in the periodic complex action theory
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Reality from maximizing overlap in the periodic complex action theory. / Nagao, Keiichi; Nielsen, Holger Bech.
In: Progress of Theoretical and Experimental Physics, Vol. 2022, No. 9, 091B01, 18.08.2022.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Reality from maximizing overlap in the periodic complex action theory
AU - Nagao, Keiichi
AU - Nielsen, Holger Bech
PY - 2022/8/18
Y1 - 2022/8/18
N2 - We study the periodic complex action theory (CAT) by imposing a periodic condition in the future-included CAT where the time integration is performed from the past to the future, and extend a normalized matrix element of an operator (O) over cap, which is called the weak value in the real action theory, to another expression (periodic time). We present two theorems stating that (periodic time) becomes real for (O) over cap being Hermitian with regard to a modified inner product that makes a given non-normal Hamiltonian (H) over cap normal. The first theorem holds for a given period t(p) in a case where the number of eigenstates having the maximal imaginary part B of the eigenvalues of (H) over cap is just one, while the second one stands for t(p) selected such that the absolute value of the transition amplitude is maximized in a case where B
AB - We study the periodic complex action theory (CAT) by imposing a periodic condition in the future-included CAT where the time integration is performed from the past to the future, and extend a normalized matrix element of an operator (O) over cap, which is called the weak value in the real action theory, to another expression (periodic time). We present two theorems stating that (periodic time) becomes real for (O) over cap being Hermitian with regard to a modified inner product that makes a given non-normal Hamiltonian (H) over cap normal. The first theorem holds for a given period t(p) in a case where the number of eigenstates having the maximal imaginary part B of the eigenvalues of (H) over cap is just one, while the second one stands for t(p) selected such that the absolute value of the transition amplitude is maximized in a case where B
KW - PSEUDO-HERMITICITY
KW - PT-SYMMETRY
KW - FORMULATION
KW - FUTURE
U2 - 10.1093/ptep/ptac102
DO - 10.1093/ptep/ptac102
M3 - Journal article
VL - 2022
JO - Progress of Theoretical Physics Supplement
JF - Progress of Theoretical Physics Supplement
SN - 2050-3911
IS - 9
M1 - 091B01
ER -
ID: 317435675