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On the quadratic Heisenberg group. (English) Zbl 1213.60123

One derives the quadratic analogue of the Weyl relations and of the Heisenberg group with one degree of freedom, in the framework of a nonlinear white noise calculus. To some extent, the paper clarifies the role of the so-called canonical commutations relations.

MSC:

60J25 Continuous-time Markov processes on general state spaces
60J45 Probabilistic potential theory
60H40 White noise theory
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References:

[1] DOI: 10.1088/1751-8113/41/30/304001 · Zbl 1145.81036 · doi:10.1088/1751-8113/41/30/304001
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[15] DOI: 10.1007/s10440-005-9000-7 · Zbl 1081.60535 · doi:10.1007/s10440-005-9000-7
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