An approximate representation of SU(2) ordered exponentials in the stochastic limit

A method of approximating an SU(2) ordered exponential U(t‖E), defined in terms of a two-dimensional input vector E (t)= E (t)E(t), E=+( E ) 2 1 2 , is suggested for the stochastic limit of strongly varying E, where ‖dE/ dt‖ ⪢ E. In the context of an “averaged” representation, where the high frequency fluctuations normally superimposed upon a relatively slowly-varying background are suppressed, U(t‖ (E) is given as a functional of E(t), suitable for use as an integrand in a functional integral with gaussian white-noise weighting.