Recent content by jfy4

Thanks for your response. You already taught me something! However, I was thinking more along the lines of something like Temple's inequality. An inequality relation using expectation values of the Hamiltonian. I have been trying to find something similar for other energies besides the...

Hi, I'm interested in learning about what would be the compliment to the Variational method. I'm aware that the Variational method allows one to calculate upper bounds, but I'm wondering about methods to calculate lower bounds on energy eigenvalues. And for energies besides the ground state if...

You want the expectation value of the Wilson Loop, ##\langle W \rangle = \text{Tr}[W e^{iS}]##. Perhaps the best way to work is to switch to a lattice regularization and visualize the Wilson Loop on a 3d lattice and see how it gives information about confinement through its perimeter and area.

For pure gauge, one can use the Wilson loop.

There are no two areas of physics that are disjoint. While it may seem inefficient and unnecessary to read those parts, you will benefit greatly be taking the time to first, convince yourself intelectually and emotionally that those topics are important and arrive at this conclusion yourself...

well, the idea I suggested implies that when we could probe those energies, we could not distinguish which theory is the correct one by different expirements. A situation where different theories predict different phenomena, some of which may be mutually exclusive, yet we observe phenomena from...

"quantum theory of angular momentum" By (author): D A Varshalovich By (author): A N Moskalev By (author): V K Khersonskii

I actually had a similar thought a little while back... I am a lattice field theoriest, and also fond of the LQG approach, and when I found out that many continuum theories can be formulated as distinct theories on the lattice and renormalize to the same conimuum limit. It got me thinking...

The two formalisms are equivalent. However, the hamiltonian formulation singles out the time variable through the definition of the canonical momentum. Any time you single something out you break a symmetry. However, while explicit lorentz invariance is broken by this, it can be recovered.

good questions. True be told I'm not entirely sure... The matrices house local configurations on a lattice, and I can't keep them all due to computer memory cost, so I want to truncate the matrices and keep as much as I can. The only way I have been doing it is with SVD. Once I preform the...

Hi, Lets say that I have a 4x4 matrix, and am interested in projecting out the most important information in that matrix into a 2x2 matrix. Is there an optimal projection to a lower dimensional matrix where one keeps most of the matrix intact as best as possible? Thanks.

my bad about the non-compactness, I skipped a beat.

True, but I was just talking about normal GR. GR can be cast into a gauge theory using tetrads and the spin connection, which has a local lorentz group symmetry.

There is another thread somewhere around here where the discussion of GR as a theory with a local symmetry group (the lorentz group) is being discussed. It's in SR/GR somewhere... But the Lorentz group (without translations) is compact and and can certainly be a local symmetry group.

I see what you mean. I had in mind though loops of the form: (0,0),(1,0)(1,n),(n+1,n),(n+1,n+1),(1,n+1)... and n can get as large as it wants. I guess I realize that there probably are large loops which don't follow these `laws' but they contribute little I suppose.