J. Phys. Soc. Jpn. 17 (1962) pp. 1100-1120  |Next Article|  |Table of Contents|
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Generalized Cumulant Expansion Method

Ryogo Kubo

(Received April 11, 1962)

The moment generating function of a set of stochastic variables defines the cumulants or the semi-invariants and the cumulant function. It is possible, simply by formal properties of exponential functions, to generaiize to a great extent the concepts of cumulants and cumulant function. The stochastic variables to be considered need not be ordinary c-numbers but they may be q-numbers such as used in quantum mechanics. The exponential function which defines a moment generating function may be any kind of generalized exponential, for example an ordered exponential with a certain prescription for ordering q-number variables. The definition of average may be greatly generalized as far as the condition is fulfilled that the average of unity is unity. After statements of a few basic theorems these generalizations are discussed here with certain examples of application. This generalized cumulant expansion provides us with a point of view from which many existent methods in quantum mechanics and statistical mechanics can be unified. ©1962 The Physical Society of Japan

URL: http://jpsj.ipap.jp/link?JPSJ/17/1100/
DOI: 10.1143/JPSJ.17.1100

References | Citing Articles (566)

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