- Exact Isospectral Pairs of PT-Symmetric Hamiltonians
- Topologically massive gravity and complex Chern-Simons terms
- Thin tubes in mathematical physics, global analysis and spectral geometry
- Mathematical models of spontaneous symmetry breaking
- A note on canonical quantization of fields on a manifold
- Asymptotics and Hamiltonians in a First order formalism
- Why are solitons stable?
- Lurie on Extended TQFT
- Liveblogging: Jacob Lurie on 2-d TQFT
- Renormalized Quantum Yang-Mills Fields in Curved Spacetime
22
Feb
08
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.