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A cohomology theory can be defined in which the Dirac operator $\not{D}$ plays the role of the exterior derivative. I'll try to describe what I know about the subject in some detail, and give you some references. For a specific choice of the Dirac operator, this theory is customarily called: "Dirac cohomology". Just for your intuition, a theory involving ...


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I can't give you the answer you're looking for, but perhaps I can offer something of some use, because gamma-gamma pair production constructs charged particles for real. We start with a two +511keV waves, each being a field-variation propagating linearly at c. We end up with electron spin and magnetic moment and the Einstein-de Haas effect, wherein in atomic ...


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First Question You are correct that we have "lost" two degrees of freedom in defining $\epsilon^+$ and $\epsilon^-$ as above. This because they are just choices of basis vectors. In QFT we usually just work with some simple basis of polarization vectors, Indeed they'll be summed/averaged over anyway when calculating the cross-section. The two "lost" ...


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A two component spinor can be geometrically interpreted as representing a point on the Riemann sphere, defined by the ratio of its two complex components, and its stereographic projection onto the xy-plane. Similarly, a four component spinor can be interpreted, by a more complicated ratio defined by its four complex components, as a point on the Riemann ...


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The spin of a quantum field is related to the representation of the Lorentz group they transform under: scalar fields transform under the trivial representation, spinors transform under the spinorial representation, gauge bosons under the vectorial representation, gravitons (if they exist) under the second-rank tensorial representation... If you restrict to ...



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