By Miroslav Silhavy
From the reports: "The booklet is great, and covers a truly wide zone (usually handled as separate themes) from a unified standpoint. […] it will likely be very worthwhile for either mathematicians and physicists." EMS e-newsletter
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Additional info for The mechanics and thermodynamics of continuous media
Sample text
Here we use the fact that K1 (B) is nothing but the average derivative 19) . 14-16) are significantly simpler in the case of Gaussian random variables. 3 Moments and Correlators in Quantum Theory The above formulas are valid in the nonquantum case. However, it should be noted that random variables become operators in the quantum case and, generally speaking, they are noncommutative. Therefore, products with different order of multipliers are distinct in the quantum case. All of them correspond to the same nonquantum product. Hence, moments and, consequently, cumulants may be defined in various ways in the quantum case. 1 Moments and the Characteristic Function Suppose we have random variables ~ 1, . . , ~n (n is arbitrary), which have the joint probability density w( ~ 1, . . , ~n)' The mean value f <~~l ... ~~n) = ~~l ... ~~nW(~l' ... , ~n)d~l ... 1) is called the moment. The characteristic function e(iu 1, ... • , iun ) = (exPCt1 f iU~~~) ) = eXPCt1 iu~~~ )W(~l" .. , ~n )d~l ... 1,2), we easily verify that the moments can be expressed in terms of the characteristic function: ): ... _m[ame(iU1, ... , iUn)] <"~l 1 Here U = °means that U1 aU~l ...