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Borchers algebra : ウィキペディア英語版
Borchers algebra
In mathematics, a Borchers algebra or Borchers–Uhlmann algebra or BU-algebra is the tensor algebra of a vector space, often a space of smooth test functions. They were studied by , who showed that the Wightman distributions of a quantum field could be interpreted as a state, called a Wightman functional, on a Borchers algebra. A Borchers algebra with a state can often be used to construct an O
*-algebra
.
The Borchers algebra of a quantum field theory has an ideal called the locality ideal, generated by elements of the form ''ab''−''ba'' for ''a'' and ''b'' having spacelike-separated support. The Wightman functional of a quantum field theory vanishes on the locality ideal, which is equivalent to the locality axiom for quantum field theory.
==References==

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