Unbounded GNS representations of a*-algebra in a Krein space

✍ Scribed by J. -P. Antoine; S. Ôta

• Publisher: Springer
• Year: 1989
• Tongue: English
• Weight: 375 KB
• Volume: 18
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00405258

✦ Synopsis

Al~traet. Given a *-algebra 9.I and a linear, nonpositive definite, functional on it, the GNS construction yields a representation of 9./ in an indefinite metric space. We show that, if the functional satisfies a suitable condition, expressed in terms of a conditional expectation on 2, then the representation space is a Krein space. This provides an abstract setup for the description of a massless quantum field theory.