Can gauge theory be rerepresented as a discrete-time stochastic process which exhibits the Markov property (i.e. a Markov process)?

 

If so, is anyone trying to do this?

 

My apologies if I'm completely off base here...

I fail to see any similarities between symmetry operations and random walks. Space and time as well as the symmetries assumed in gauge theory are continous, not discrete. Also, quamtum mechanics is -with the exception of the measuring process- strictly deterministic and in no way random. Given an initial state you know -in theory- exactly how it develops over time. That´s what the Hamiltonian is for.

 

I think you are what you called "completely off base". But maybe you could elaborate a bit on what you actually meant. I don´t really understand it.

Yeah, thought so. Guess I need to refine my ideas a bit more, or just discard them entirely.

 

One of these days I'll actually get around to writing a model... my own universe from scratch kind of thing.

 

My assumption is that the system "normalizes" and its behavior moves from a period of extreme state flux to relatively minor and gradual changes as a stochaic process settles upon a more fixed kind of pattern. But yeah, I can't really explain jack with this model, can I... *sigh*

 

Yeah, speculative propositioning doesn't really work at all, does it? Needs more, uhh, reality...

He is not completely 'off base'. Lattice QCD is a way of simulating Quantum Chromodynamics (a gauge theory) on a space-time lattice of points (which included discrete time). If fact the discretization is a valid regularization of the divergences in the theory, and lattice QCD is a very valid (most valid?) way of looking at QCD theoretically. These simulations are also probabilistic and very often involve Markov Chains.

 

http://en.wikipedia.org/wiki/Lattice_gauge_theory