The Casimir chaos map for $U(N)$

Rok, strany: 1993, 81 - 88

The generalized number processes of $N$-dimensional quantum stochastic calculus form a representation of the Lie algebra $\Scr L$ of $U(N)$. Their stochastic differentials form a second such representation. Associated with each Casimir element $C$, we construct a Casimir process $(C_t: t\in\Bbb R₊)$ using the first representation, and a Casimir chaos process combining the second with an iterated integral which is defined naturally on the tensor algebra over $\Scr L$ but is shown to extend to the center $\Scr Z$ of the universal enveloping algebra in a natural way. The Casimir chaos process of $C$ is the Casimir process of the image of $C$ under a bijective linear map on $\Scr Z$.

ISO 690:

Hudson, R., Parthasarathy, K. 1993. The Casimir chaos map for $U(N)$. In Tatra Mountains Mathematical Publications, vol. 3, no.2, pp. 81-88. 1210-3195.

APA:

Hudson, R., Parthasarathy, K. (1993). The Casimir chaos map for $U(N)$. Tatra Mountains Mathematical Publications, 3(2), 81-88. 1210-3195.