Glauber Coherent States, Crystals, Ferromagnets, Superconductors, Higgs-Goldstone bosons

On Jun 27, 2013, at 12:04 AM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

there are results in A that may be more relevant because it deals with bound states.
None of the S-Matrix papers deal with mundane electrical power engineering
i.e. quasi-static non-radiative near fields of say capacitors, solenoids, electric motors and dynamos, power lines with small radiative leaking.
Of course classical EM provides a practical theory for electrical engineers, but our problem is to see how this very practical world fits in with QED S-Matrix. We are not interested here in scattering input real particles into output real particles. We are interested rather in the quantum description of the near EM fields.

Also, ordinary S-Matrix never deals with coherent Glauber states only with Fock states.

Of course a classical current Ju makes Glauber coherent states - but for near fields the photons are virtual not real.

The Gorkov method for BCS superconductor is more to the point - there the Glauber coherent states of Cooper pairs is an emergent non-perturbative effect from summing I think and infinity of tree Feynman diagrams? So that is one way to think of spontaneous breakdown of symmetry in many particle systems.

Note that the key LNIF metric representations for Schwarzschild, de Sitter, Kerr are all Glauber coherent states of virtual gravitons.

Ordinary space crystal lattice ground states are Glauber coherent states of virtual phonons f = 0 & ki ~ n/ai, ai lattice spacings of unit cell.

Ferromagnetic ground states are Glauber coherent states of virtual spin wave quanta

In contrast, superconductor ground states are Glauber coherent states of real Cooper pairs?

Superfluid helium 4 ground state is a Glauber coherent state of virtual phonons as well f = 0 with a continuum of ki.

Except for the Cooper pairs - the we have above ground states whose Landau-Ginzburg order parameters are Glauber coherent states of the massless Goldstone boson in virtual off-mass-shell form.

In the post-inflation vacuum we also have Glauber coherent states of virtual massive Higgs bosons.

Actually to be more precise the order parameter is in simplest case e.g. center of mass of Cooper pair

<0|Psi|0> = R(x)e^iS(x)

Psi is a second quantized annihilation operator in ordinary spacetime

|0> is the broken symmetry ground state

x = ordinary 3D + 1 event

R(x) is a condensate of massive Higgs bosons

S(x) the coherent state is a condensate of massless Goldstone particles.

|R(x)e^IS(x)> is the Glauber coherent state


On Jun 26, 2013, at 11:26 PM, Ruth Kastner <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

I had it at one time but can't seem to find it. But as I recall it is superseded by the two that I sent you, which give a more comprehensive and general treatment.

R

> From: This email address is being protected from spambots. You need JavaScript enabled to view it.
> Subject: Davies paper A
> Date: Wed, 26 Jun 2013 23:20:36 -0700
> To: This email address is being protected from spambots. You need JavaScript enabled to view it.
> > Do u have it? Apparently it's a prequel to the two you sent.