Classical and Quantum Dynamics by Walter Dittrich & Martin Reuter

Author:Walter Dittrich & Martin Reuter
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(18.1)

Here Q(t) and P(t) stand for arbitrary c-number functions (“sources”) and T denotes the time-ordering operation with respect to the Heisenberg operators q(t) and p(t). When acting on a string of operators with different time arguments it orders the operators in such a way that the time arguments increase from the right to the left. The exponential in (18.1) should be interpreted as a power series, and in each term T acts according to the above rule:

(18.2)

The advantage offered by the introduction of external sources is that any number of operators between brackets can be generated by a simple functional differentiation, e.g.,

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