# Hall's transformation via quantum stochastic calculus

Paula Cohen; Robin Hudson; K. Parthasarathy; Sylvia Pulmannová

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 147-155
- ISSN: 0137-6934

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topCohen, Paula, et al. "Hall's transformation via quantum stochastic calculus." Banach Center Publications 43.1 (1998): 147-155. <http://eudml.org/doc/208833>.

@article{Cohen1998,

abstract = {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.},

author = {Cohen, Paula, Hudson, Robin, Parthasarathy, K., Pulmannová, Sylvia},

journal = {Banach Center Publications},

keywords = {Hall's transformation; Bargmann-Fock representation; heat kernel; Lie group; Lie algebra; universal enveloping algebra; deformation quantization; stochastic flow; quantum stochastic calculus; Dyson perturbation expansion},

language = {eng},

number = {1},

pages = {147-155},

title = {Hall's transformation via quantum stochastic calculus},

url = {http://eudml.org/doc/208833},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Cohen, Paula

AU - Hudson, Robin

AU - Parthasarathy, K.

AU - Pulmannová, Sylvia

TI - Hall's transformation via quantum stochastic calculus

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 147

EP - 155

AB - 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.

LA - eng

KW - Hall's transformation; Bargmann-Fock representation; heat kernel; Lie group; Lie algebra; universal enveloping algebra; deformation quantization; stochastic flow; quantum stochastic calculus; Dyson perturbation expansion

UR - http://eudml.org/doc/208833

ER -

## References

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