Paper I: The Spontaneous breaking of the Continuous Particle Exchange Symmetry
Paper II: The Supersymmetric QED with the scalar supercharge
Paper III: The Linear Zeeman effect in the molecular positronium Ps2 (dipositronium)
Paper IV: The positron-positron Moller scattering: call for the experiment
Paper V: Spontaneous symmetry lowering of the SO(N,3N) metric field interacting with the massles spinor
keywords: e+e+ moller scattering, supersymmetry, scalar supercharge, high density positron plasma, dipositronium spin states, positron statistics, unstable antiworld.
The idea to exchange fields by rotations in 4N dimensional space is IMHO brand new,
and it is realized in the linked papers. Overall the project has taken nearly 15 years since 1999, when I 1st time heard prof. Berry talk about continuous particle exchange by the mathematical analog of the belt trick. Actually I have tons of related calculations; most of them are related to the embedding of the tensor product of SO(4) and O(N) to SO(4N).
After all, the theory arrives at the super-symmetric electro-dynamics with charge conjugation taking bosons to fermions, positive charge to negative charge, changing the sign of the parity and the spin. In other words, positron and electron have same mass and spin; positron and electron have opposite charge, parity and statistics.
I’m not that ambitious to state that this theory more than just mathematical exercise related to the foundations of the Pauli principle ( spin-statistics theorem ). Basically I say that one can go around the Pauli principle if the statistics can be changed by the charge conjugation.
The experimental data on two positron systems is very limited. As of September 4 2014 there is no experimental data on positron-positron scattering; no experimental data on positron-positronium scattering; no experimental data on positronium-positronium scattering; no experimental data on Positronium molecule (Ps2) ground state magnetization.
There is now lot of efforts to make positronium laser; it requires high density cold positronium plasma; possibly the condensed state of the positronium or positronium molecules. Joint Quantum Institute. “Stimulated mutual annihilation: How to make a gamma-ray laser with positronium.” ScienceDaily. ScienceDaily, 1 May 2014.
Medical application use positron emission tomography and annihilation radiation tomography. The opposite Parity of electron and positron put a constrain on radiation polarization. However the annihilation events are not coherent. All symmetries of the positronium are listed in the text book. Fresh reference.
The positronium Hyper-fine structure is analysed many years, now at \alpha^7 order by Adkins&Fell . The Rich’s review gives all the data 1930-1980. The L=1 state of the positronium molecule was predicted by K. Varga, J. Usukura, and Y. Suzuki PRL(1998), and L=1 to L=0 transition (251nm) was measured recently by D. B. Cassidy et all PRL(2012).
I hope that the Positronium molecule (Ps2) life-time can bring some evidences in favor of the theory. Here is my 2nd paper on the dipositronium magnetic moment. The linear Zeeman effect is predicted for some of $S=1, S=2$ states; if the above theory is correct, then $S=1$ becomes the ground state; it can be unambiguously identified by the linear Zeeman split.
The N=1, L=0, S=0 state of the positronium is the short living (125ps); the N=1, L=0, S=1 state of the positronium is the long living (142ns). The posironium molecule (Ps2) lifetime is in wide range 0 – 150ns with both L=0 and L=1 at S=0, see D. B. Cassidy & A. P. Mills publications in Nature(2007) and PRL(2012). This is very much puzzling; basically they did not consider any direct annihilation inside the Ps2 moleciule. They assume Ps2 molecule made from two positronium “atoms” with S=1 M=1 and S=1 M=-1. Therefore the Ps2 molecule lifetime is determined by dissociation Ps2 → o-Ps + o-Ps, then flip o-Ps → p-Ps, then annihilation p-Ps→2γ
I propose that the positronium molecule is made from ortho- and para-positronium “atoms”; but annihilation is limited once they are coupled. So the process become Ps2 → o-Ps + p-Ps, then annihilation p-Ps→2γ; in this model the Ps2 lifetime is just the dissociation time. I hope to continue the parity analysis for all processes as my next project.