Formulation of Complex Action Theory(General and Mathematical Physics)

概要

論文の詳細を見る
We formulate a complex action theory which includes operators of coordinate and momentum q^^^ and p^^^ being replaced with non-hermitian operators q^^^_<new> and p^^^_<new> and their eigenstates |q>_<new> and |p>_<new> with complex eigenvalues q and p. Introducing a philosophy of keeping the analyticity in path integration variables, we define a modified set of complex conjugate, real and imaginary parts, hermitian conjugates and bras, and explicitly construct q^^^_<new>, p^^^_<new>, |q>_<new> and |p>_<new> by formally squeezing coherent states. We also pose a theorem on the relation between functions on the phase space and the corresponding operators. Only in our formalism can we describe a complex action theory or a real action theory with complex saddle points in the tunneling effect etc. in terms of bras and kets in the functional integral. Furthermore, in a system with a non-hermitian diagonalizable bounded Hamiltonian, we show that the mechanism to obtain a hermitian Hamiltonian after a long time development proposed in our paper [Prog. Theor. Phys. 125 (2011), 633] works also in the complex coordinate formalism. If the hermitian Hamiltonian is given in a local form, a conserved probability current density can be constructed with two kinds of wave functions.
理論物理学刊行会の論文
2011-12-25