A QUANTUM ANALOG OF HUNTS REPRESENTATION THEOREM FOR THE GENERATOR OF CONVOLUTION SEMIGROUPS ON LIE-GROUPS

• 成果类型: Article
• 署名作者: BARCHIELLI, A; LUPIERI, G
• 署名单位: Istituto Nazionale di Fisica Nucleare (INFN)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01212558
• 发表日期: 1991
• 页码: 167-194
• 关键词: dynamical semigroups; stochastic calculus; probability

摘要

In quantum mechanics certain operator-valued measures are introduced, called instruments, which are an analogue of the probability measures of classical probability theory. As in the classical case, it is interesting to study convolution semigroups of instruments on groups and the associated semigroups of probability operators. In this paper the case is considered of a finite-dimensional Hilbert space (n-level quantum system) and of instruments defined on a finite-dimensional Lie group. Then, the generator of a continuous semigroup of (quantum) probability operators is characterized. In this way a quantum analogue of Hunt's representation theorem for the generator of convolution semigroups on Lie groups is obtained.