Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebra with indefinite involution and its representation in Krein space   It is often inevitable to introduce an indefinite-metric space in quantum
field theory, for example, which is explained for the sake of the manifestly
covariant quantization of the electromagnetic field. We show two more evident
mathematical reasons why such indefinite metric appears. The first idea is the
replacement of involution on an algebra. For an algebra ${\cal A}$ with an
involution $\sdag$ such that a representation of the involutive algebra $({\cal
A},\sdag)$ brings an indefinite-metric space, we replace the involution $\sdag$
with a new one * on ${\cal A}$ such that $({\cal A},*)$ is a well-known
involutive algebra acting on a representation space with positive definite
metric. This explains that non-isomorphic two involutive algebras are
transformed each other by the replacement of involution. The second is that a
covariant (Hilbert space) representation $({\cal H},\pi,U)$ of an involutive
dynamical system $(({\cal A},*),{\bf Z}_{2},\alpha)$ brings a Krein space
representation of the algebra ${\cal A}$ with the replaced involution. For
example, we show representations of abnormal CCRs, CARs and pseudo-Cuntz
algebras arising from those of standard CCRs, CARs and Cuntz algebras.

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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph