22
Feb
08

This week in the arXivs…


1 Response to “This week in the arXivs…”


  1. Monday, 25 Feb 2008; \09\UTC\UTC\k 09 at 20:44:50 UTC

    I’d like to make a comment about the article “Exact Isospectral Pairs of PT-Symmetric Hamiltonians”.

    The Hamiltonian of a system (regardless of PT-symmetry or not) can be seen as a “natural Laplacian operator on some manifold”, i.e., it can be treated as the Laplacian of a given manifold.

    In this sense, “isospectral Hamiltonians” would be equivalent to saying isospectral manifolds.

    These manifolds would, in some sense, represent the Configuration Space of these Hamiltonians.

    The point is: these distinct configuration manifolds yield different Phase Spaces, which have unequal quantization rules: Phase Space Quantization. Nowadays, Phase Space Quantization has become Geometric Quantization and Deformation Quantization.

    Anyway… the weather is changing, i’m in pain… and now i’m rambling too.😦

    Maybe i’ll have something useful to say when my brain comes back online…😛

    []’s.


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