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Title:
Walks in the Hilbert space
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Abstract:
The pair of integrable many-body systems enjoys the duality at classical and quantum level when the coordinates get interchanged with the variables yielding the spectrum. Similar questions can be posed for the non-integrable systems as well. Since the wave function as a function of coordinates allows the path integral representation one could question if the dual "path integral" representation in the Hilbert space for the wave function of the quantum system is possible. We present the examples of such representation. Some lessons for representation of Hilbert space in terms of paths on the graphs from the theory of random networks will be discussed. The possible holographic picture behind this realization of the Hilbert space will be mentioned.
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