Quantum phenomena via complex measure: Holomorphic extension

Abstract

The complex measure theoretic approach proposed earlier is reviewed and a general version of density matrix as well as conditional density matrix is introduced. The holomorphic extension of the complex measure density (CMD) is identified to be the Wigner distribution function of the conventional quantum mechanical theory. A variety of situations in quantum optical phenomena are discussed within such a holomorphic complex measure theoretic framework. A model of a quantum oscillator in interaction with a bath is analyzed and explicit solution for the CMD of the coordinate as well as the Wigner distribution function is obtained. A brief discussion on the assignment of probability to path history of the test oscillator is provided.

On Noncontextual, Non-Kolmogorovian Hidden Variable Theories

“…In the second approach to extending the range of the probability measure, one goes even further, allowing it to take on complex values, as proposed by Ivanović (1978); Youssef (1991Youssef ( , 1994Youssef ( , 1995Youssef ( , 1996; Miller (1996); Srinivasan and Sudarshan (1994); and Srinivasan (1995Srinivasan ( , 1998Srinivasan ( , 2006. 10 Definition 11.…”