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Natural Science Forum / Physics / Particle Physics / October 2005Baryons as Third Rank Antisymmetric Tensors
Hello again: I just posted some further materials at http://home.nycap.rr.com/jry/FermionMass.htm, regarding my very strong suspicion that baryons are third rank antisymmetric tensors, including the basic Feynman and scattering diagrams for a third rank antisymmetric tensor which you will see seem to be suggestive of a baryon. Jay. _____________________________ Jay R. Yablon Email: jyablon@nycap.rr.com | Hello again: | [quoted text clipped - 3 lines] | basic Feynman and scattering diagrams for a third rank antisymmetric tensor | which you will see seem to be suggestive of a baryon. Jay, I was reading in Weinberg's "Supersymmetry" book that spinors can't have a tensor representation. So if a baryon is a composite of three spinors (quarks), how can we have a tensor representation of a single baryon that is a composite fermion? What am I missing? Now, I understand that bosons composed of two spinors can have a tensor representation. FrediFizzx http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps http://www.vacuum-physics.com Fred, I don't think Weinberg is necessarily saying this. For example, the current for a fermion is J^u = (psi-bar gamma^u psi) where gamma^u are the Dirac matrices. J^u of course, is a four-vector (first rank tensor) in spacetime, and represent the current originating from the Fermion. The baryons I am constructing follow a similar path. In both cases, a psi-bar is hooked together with psi via a Dirac gamma, and it is this pairing that allows a tensor formulation. Jay. _____________________________ Jay R. Yablon 910 Northumberland Drive Schenectady, New York 12309-2814 Phone / Fax: 518-377-6737 Email: jyablon@nycap.rr.com > | Hello again: > | [quoted text clipped - 20 lines] > > http://www.vacuum-physics.com | Fred, | [quoted text clipped - 5 lines] | together with psi via a Dirac gamma, and it is this pairing that allows a | tensor formulation. Oops, maybe I phrased that poorly? Let me quote what he actually says in chapter 31; "Supergravity necessarily involves spinor as well as tensor fields, so we will have to describe gravitational fields in terms of a vierbein (or tetrad) e^a_u(x) rather than a metric,..." So why would he be specifying spinor and tensor fields separately here? Then in the Appendix for 31 he says; "Unlike vectors and tensors, spinors have a Lorentz transformation rule that has no natural generalization to arbitrary coordinate systems." He does seem to be saying that spinors are different from vectors and tensors. Well, it just seems obvious to me since spinors do have a unique direction. So maybe it is not that baryons are a third rank antisymmetric tensor but this tensor is representing something about the baryon? Similar to how J^u is the current for a fermion? FrediFizzx | > | Hello again: | > | [quoted text clipped - 20 lines] | > | > http://www.vacuum-physics.com So maybe it is not that baryons are a third rank > antisymmetric tensor but this tensor is representing something about the > baryon? Similar to how J^u is the current for a fermion? Yes, Fred, I like better, your way of putting this. Jay. Hi Fred Jay and all > | Fred, > | [quoted text clipped - 30 lines] > antisymmetric tensor but this tensor is representing something about the > baryon? Similar to how J^u is the current for a fermion? Weinberg in Grav&Cosmo pg 58, 1st paragraph, discusses introducing spinors, in the Lorentz transform to account for "1/2 integer spin" denoted by omega in 2.12.5, and is anti-symmetric. Later on pg 365, "The Tetrad Formalism" he shows how "spinors" can be incorporated into GR. For interest see pg 367 where he mentions "dual classification". ((IMHO I'm uncomfortable with spinors together with a continuum, look at his 2.12.5 again and see the condition, |omega^a_b| << 1 that's a bit of a "shoe horn")) Anyway he's trying to lay the ground work for relativistic quantum field theory. > FrediFizzx Regards Ken S. Tucker |
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