Abstract
The exponential operator, i.e. the exponential function of an operator, defined in (1.19) by way of a series expansion, is of paramount interest in mathematical physics. In view of its importance, we discuss in this chapter some useful algebraic operations involving an exponential operator. The operations discussed here are (i) the parametric differentiation of an exponential operator, (ii) its reduction to a polynomial when the exponent is finite-dimensional, (ii) similarity transformation, defined below, by an exponential operator, (iii) the operation of disentangling an exponential, and (iv) evaluation of time-ordered exponential integral.
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