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# Accession Number:

## AD0603619

# Title:

## STATISTICAL DESCRIPTIONS OF FREE BOSON FIELDS,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Report Date:

## 1964-08-01

# Pagination or Media Count:

##
21.0

# Abstract:

## Two new methods of describing statistical light beams have recently been published. Glauber has introduced the Prepresentation of boson field density matrices, and Sudarshan has developed a probability functional approach which is claimed to imply an equivalence between the classical and quantum mechanical descriptions of statistical light beams. This note demonstrates that using conventional stochastic process methods in the Heisenberg picture to describe a light beam produced by a statistical ensemble of classical c-number sources is equivalent to representing the statistical state of the light beam by a density matrix having a P-representation. The relation between the classical and quantum statistical descriptions implied by Sudarshans probability functional approach is shown to be purely formal and without physical meaning. Sudarshans statement that the probability functional method can be used to prove that all the correlation functions of the beam determine its density matrix is demonstrated to be incorrect. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#