A Projection Operators in Quantum Statistical Mechanics

APPENDIX 1 l.A PROJECTION OPERATORS IN QUANTUM STATISTICAL MECHANICS 

In quantum mechanics observables are represented by linear Hermitian operators A, which change in time according to the equation of motion 

A(t)y and (A(/)A+(0) are not equal, but are complex conjugates of one another. Although a projection-operator formalism for these one sided correlation functions can be developed, it is more convenient for the purposes of comparing with classical correlation functions to deal with the symmetrized function 

These are real quantities that go in the classical limit ti — 0 to the classically defined correlation function. It is then possible to define the scalar product of two Hermitian operators as 

Then the whole formalism of this chapter can be applied to evaluate (/l+(0)/l(fX s. 

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