Let ω be any normal state on the CCR‐algebra, and τχ the gauge transformation corresponding to the continuous character χ on the test function space as an Abelian group; denote by K the set of these characters; then we prove that the linear hull of {ω0τχ‖χ‐K} is norm dense in all normal states. It is also proved that the theorem is in general false if we take the convex hull.
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© 1975 American Institute of Physics.
1975
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