The heat flow of the CCR algebra
| dc.creator | Arveson, William | |
| dc.date | 2000-05-24 | |
| dc.date.accessioned | 2026-07-07T04:35:32Z | |
| dc.date.available | 2026-07-07T04:35:32Z | |
| dc.description | Let P and Q be the canonical operators acting on the Hilbert space of all L^2 functions on the real line, defined appropriately on a common dense domain. The derivations D_P(A) = i(PA - AP) and D_Q(A) = i(QA - AQ) act on the *-algebra of all integral operators having smooth kernels of compact support, for example, and one may consider the noncommutative "Laplacian" L(A) = D_P^2(A) + D_Q^2(A), as a linear mapping of this *-algebra into itself. L generates a semigroup of normal completely positive maps on B(H), and we establish some basic properties of this semigroup and its minimal dilation to an E_0-semigroup. In particular, we show that the minimal dilation is pure, has no normal invariant states, and we discuss the significance of those facts for the interaction theory developed in a previous paper (appearing in the current issue of Comm. Math. Phys.). There are similar results for the canonical commutation relations with n degrees of freedom, n = 2, 3, .... | |
| dc.description | 12 pages typeset | |
| dc.identifier | https://arxiv.org/abs/math/0005250 | |
| dc.identifier | http://arxiv.org/abs/math/0005250 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59281 | |
| dc.subject | Operator Algebras | |
| dc.title | The heat flow of the CCR algebra | |
| dc.type | text |