A Gauge Model for Quantum Mechanics on a Stratified Space
نویسندگان
چکیده
منابع مشابه
A gauge model for quantum mechanics on a stratified space
In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified Kähler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure yields a costratified Hilbert space, that is, a Hilbert spa...
متن کاملA lattice gauge model for quantum mechanics on a stratified space
In the Hamiltonian approach on a single spatial plaquette, we construct a quantum lattice gauge theory which incorporates the classical singularities. The reduced phase space is a stratified Kähler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure furnishes a costratified Hilbert space, that is, a Hilbert sp...
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In this note we present a operator formulation of gauge theories in a quantum phase space which is specified by a operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport) and Wilson line (parallel transport) which enables us to construct a gauge theory in a simple way. We illustrate the formulation by a discussion of the Higgs m...
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An Abelian gerbe is constructed over classical phase space. The 2–cocycles defining the gerbe are given by Feynman path integrals whose integrands contain the exponential of the Poincaré–Cartan form. The U(1) gauge group on the gerbe has a natural interpretation as the invariance group of the Schroedinger equation on phase space.
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We construct a U(1) gerbe with a connection over a finite–dimensional, classical phase space P. The connection is given by a triple of forms A,B,H : a potential 1–form A, a Neveu–Schwarz potential 2–form B, and a field–strength 3–form H = dB. All three of them are defined exclusively in terms of elements already present in P, the only external input being Planck’s constant ~. U(1) gauge transfo...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2008
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-008-0693-0