Covariance algebras in field theory and statistical mechanics
Covariance algebras in field theory and statistical mechanics
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DOI：
10.1007/bf01645459
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发表时间：
1966-02
影响因子：
2.4
通讯作者：
S. Doplicher;D. Kastler;D. W. Robinson
中科院分区：
文献类型：
--
作者：
S. Doplicher;D. Kastler;D. W. Robinson
从C *-代数和的自同构的局部紧群T出发，构造了一个“协变代数“，其性质是相应的 *-表示与的协变表示一一对应. *-表示，其中的自同构是连续酉实现的。我们进一步为相对论场论构造了一个代数，它给出了的 *-表示，其中时空平移的谱包含在V中。将超选扇区可数出现的问题表述为谱上的一个条件。最后，我们考虑的协方差algebuilt与空间平移单独和显示其相关性的讨论平衡态的统计力学，即我们恢复在这个框架中的唯一性的真空，不可约性和弱聚类属性的等价性。
Starting from aC*-algebraand a locally compact groupTof automorphisms ofwe construct a “covariance algebra”with the property that the corresponding *-representations are in one-to-one correspondence with covariant representations ofi.e. *-representations ofin which the automorphisms are continuously unitarily implemented. We further construct for relativistic field theory an algebrayielding the *-representations ofin which the space time translations have their spectrum contained inV. The problem of denumerable occurence of superselection sectors is formulated as a condition on the spectrum of. Finally we consider the covariance algebrabuilt with space translations alone and show its relevance for the discussion of equilibrium states in statistical mechanics, namely we restore in this framework the equivalence of uniqueness of the vacuum, irreducibility and a weak clustering property.