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Hall's transformation via quantum stochastic calculus

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Cohen P. B., Hudson R. L., Parthasarathy K. R., Pulmannová S.

Banach Center Publications

1998

tom 43

nr 1

147-155

It is well known that Hall's transformation factorizes into a composition of two isometric maps to and from a certain completion of the dual of the universal enveloping algebra of the Lie algebra of the initial Lie group. In this paper this fact will be demonstrated by exhibiting each of the maps in turn as the composition of two isometries. For the first map we use classical stochastic calculus, and in particular a stochastic analogue of the Dyson perturbation expansion. For the second map we make use of quantum stochastic calculus, in which the circumambient space is the complexification of the Lie algebra equipped with the ad-invariant inner product.

Ograniczanie wyników

1 Banach Center Publications

1 Cohen P. B.

1 Hudson R. L.

1 Parthasarathy K. R.

1 Pulmannová S.

1 1998

Wyniki wyszukiwania

Hall's transformation via quantum stochastic calculus