I think this paper might address the "coupling term in the Hamiltonian" you're asking about.
http://amsdottorato.unibo.it/3777/1/dalmonte_marcello_tesi.pdf 1.1.1 Mermin-Wagner-Hohenberg theorem One of the main general results in 1D physics is related to the so called spontaneous symmetry breaking (SSB) mechanism[12, 13, 14]. In statistical mechanics and quantum field theory, when a certain ground state exhibits less symmetry than the related Hamiltonian, one says that a certain sym- metry has been broken: that’s the essence of SSB. While various interesting phenomena, such as the emergence of superconductivity, can be explained in these terms, the most intuitive view on the subject is usually associ- ated with the emergence of spontaneous magnetization in solids: given a certain ordered configuration C which minimizes the energy functional, an exactly opposite configuration C ′with the same energy always exists. Nonetheless, the state of the system is not invariant under transformation C↔C′, and thus this exchange symmetry is broken[13]. The curious point is, in low dimensional systems, SSB suffers from a no-go theorem known as the Mermin-Wagner(MW) theorem (or Mermin-Wagner-Hohenberg(MWH) theorem). In their seminal paper [1 5], Mermin and Wagner showed that the Heisenberg model cannot display a finite magnetization m(h) at finite temperature in one and two dimension, and at zero temperature in one dimension, if the interac- tion coefficients are short-range... On Fri, Mar 14, 2014 at 8:16 PM, Bob Cook <frobertc...@hotmail.com> wrote: > Jones said: > > In order to have excess energy to shed, there must exist sequential RPF >>> >> between two of the three protons, which convert a tiny bit of nuclear mass > to spin energy. Degenerate spin of trihydrogen ions must be pumped back > from > low-to-high for net excess. Such pumping is presumed to be inherent in the > underlying RPF reaction, via QCD. << > > The distribution of small amounts of spin energy crops up again. And in a > magnetic field the spin states are separated by a greater energy gap, > potentially giving a variety of resonant frequencies that work to effect > transitions. > > Jones, what do the coupling term in the Hamiltonian look like? Any > references you know of? > > > Bob > ----- Original Message ----- From: "Jones Beene" <jone...@pacbell.net> > To: <vortex-l@eskimo.com> > Sent: Friday, March 14, 2014 7:57 PM > Subject: RE: [Vo]:Quote of the day > > > > From: Kevin O'Malley > > It is compelling that the "protonated molecular hydrogen or > H3+, and it > is the most abundant or second most abundant ion in the > Universe, so it is > very common." It is also compelling that RPF is the most > common fusion > reaction in the universe....I consider RPF to be the > Occham's Razor theory: Simplest is best. > > You are an intelligent observer :-) > > The Wiki entry on "trihydrogen" has supporting details - but of course, > does > not consider the putative case where one of the three protons could be in > the very tight or redundant ground state to begin with - having the other > two protons electrostatically bound to it. This would be in a "fractional > trihydrogen anion." > > In effect, two nearly free protons could be mobile around a third, instead > of a balanced triangular arrangement as often pictured; but the two have no > identifiable electron of their own. The electron orbitals of the third are > presumed to be very close geometrically such that this molecule would be > very small. This would promote the RPF reaction in which two protons > continually "try to fuse" but cannot. > > The LENR version of trihydrogen RPF is suggested to exist where excess > energy is seen due to the Lamb Shift, operating at Terahertz frequencies > (it > is a very low-energy reaction, and requires rapid sequential activity to > supply excess energy without gamma radiation). > > Two different spin configurations for H3+ are possible, ortho and para. > Ortho-H3+ has all three proton spins parallel, yielding a total nuclear > spin > of 3/2. Para-H3+ has two proton spins parallel while the other is > anti-parallel, yielding a total nuclear spin of ½ and it is slightly lower > energy. > > In order to have excess energy to shed, there must exist sequential RPF > between two of the three protons, which convert a tiny bit of nuclear mass > to spin energy. Degenerate spin of trihydrogen ions must be pumped back > from > low-to-high for net excess. Such pumping is presumed to be inherent in the > underlying RPF reaction, via QCD. > > More on that later. > > Jones > >
