Tuesday, July 05, 2011

Theta terms and asymptotic behavior of gauge potentials

[ See QED and QCD theta angles, and asymptotic boundary conditions in gauge theory for more discussion. ]

This is the sequel to an earlier paper on physical effects associated with the QED theta angle. Unfortunately, field configurations which would yield theta-dependent effects are not realizable in the lab, based on general considerations discussed in the new paper. There could, however, be small non-perturbative effects sensitive to theta despite the lack of topology in QED (maps from S^3 to U(1) are all topologically trivial).


Theta terms and asymptotic behavior of gauge potentials in (3+1) dimensions

We describe paths in the configuration space of (3+1) dimensional QED whose relative quantum phase (or relative phase in the functional integral) depends on the value of the theta angle. The final configurations on the two paths are related by a gauge transformation but differ in magnetic helicity or Chern-Simons number. Such configurations must exhibit gauge potentials that fall off no faster than 1/r in some region of finite solid angle, although they need not have net magnetic charge (i.e., are not magnetic monopoles). The relative phase is proportional to theta times the difference in Chern-Simons number. We briefly discuss some possible implications for QCD and the strong CP problem.


David Coughlin said...

Can we estimate it on the lattice?

RKU1 said...

I wonder what that Gopnik fellow would say about this...

David Coughlin said...

Trade secret?

ohwilleke said...

"gauge potentials that fall off no faster than 1/r in some region"

I've never seen the issue put that way before.  I find it notable because dark matter effects are equivalent to gravitational fields declining as 1/r rather than 1/r^2 in a region, and wasn't aware of any process with gauge potentials that fell off at a 1/r rate until now.

steve hsu said...

You might be mixing up forces and potentials ;-)

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