Fiber bundles in quantum physics

Journal of Mathematical Physics

Volumn 43, Issue 3, 2002, Pages 1323-1339

  Sen, R N ^a   Sewell, G L ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035981864     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1447309     Document Type: Article

References (40)

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8. That is, a fiber bundle in which the fiber is an infinite-dimensional complex Hilbert space. It should be noted that, in the mathematical literature, the term Hilbert bundle is often used to denote a somewhat larger class of spaces. See R.C. Fabec, Fundamentals of Infinite-Dimensional Representation Theory, (Chapman and Hall/CRC, Boca Raton, FL, 2000), and references cited therein.
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23. For infinite systems, this is more generally applicable than the Heisenberg picture. The essential point here is that the Heisenberg picture of the dynamics of infinite systems corresponds to automorphisms of their algebras of observables, which exist only for particular models, e.g., those of lattice systems with finite range interactions. For details, see Ref. 20 and articles cited therein.
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25. A(̇) = ω(A*(̇)A)/ω(A*A), for all elements A of Θ. It is thus a subset, possibly a proper one, of the mathematical state space, given by the positive, normalized, continuous linear functionals on Θ.
26. Λ, and ensures that the state cannot harbor an infinite number of particles in a bounded spatial region.
27. n is the algebra of n × n matrices. It is a stronger property than positivity because of quantum interference, and is naturally required in the present physical context. See Refs. 26 and 27.
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32. The state ω is primary if the center of the von Neumann algebra π(Θ)″ is trivial.
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