- 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
It's Equal, but It's Different... 
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.