Indefinite-metric quantum field theory and operator algebra

Details Indefinite-metric quantum field theory and operator algebra Indefinite-metric quantum field theory and operator algebra

2006-08-03

arxiv.org/abs/math/0608076v2

Mathematics

Operator Algebras

Scientific paper

It is often inevitable to introduce an indefinite-metric space in quantum field theory. There is a problem to determine the metric structure of a given representation space of field operators. We show the systematic method to determine such indefinite-metric explicitly. At first, we choose a new involution $*$ of field operators instead of the original involution $\sdag$ such that there is a Hilbert space $({\cal H},<\cdot|\cdot>)$ with the positive-definite metric $<\cdot|\cdot>$ which is consistent with $*$. Next we find another hermitian form $(\cdot|\cdot)$ on ${\cal H}$ such that $({\cal H},(\cdot|\cdot))$ is a Krein space and $(\cdot|\cdot)$ is consistent with $\sdag$. We apply this method to various models and show that our results coincide with known results.

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