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Spidergrams and particle interactions!

  1. Aug 22, 2003 #1
    In this post I would like to discuss the "weight-principle". This is a rule-of-thumb principle, related to the power-counting principle of renormalisation, which says that different types of particles are given different "interaction weights" specifically the following:

    gauge boson:2

    and also the derivative is given a weight of 2. The weight principle says that the only interactions that can occur are those who weights add up to 8. This includes all interactions from Yang-Mills Theory (where we write S for the Dirac Spinor spinor):

    Action = (DA)(DA) + AA(DA) + AAAA + SDS + SAS

    If we call the "interaction weight" of a particle, W, the number of indices of that particle is also given by W. (The indices must have values from 1 to 8). The 'spin' of the particle we shall define in a different way to normal as 2-W/2. This gives fermions spin 1/2 as we want. We find that the 2 extra indices of the fermion actually form an index giving the generation number.

    The total number of components of the fermion field, for example, which has 3 indices is 8x7x6/(3!) which gives 56, and because a fermion field has 8 inpedpendent real components and 56=8x7, this gives 7 fields in total.

    By examing the total number of components of each of the 4 different kinds of fields, if the "weight principle" holds then there can be no more than 1 graviton, 2 gravitinos (with half the components of a fermion), 7 gauge-bosons, and 7 fermions.

    So we can account for these observed FREE particles: graviton, photon, W+,W-,Z0 weak gauge bosons, (+3 more gauge-bosons in an SU(2) representation),the 3 generations of leptons and neutrinos.

    But we CAN'T account for quarks and gluons. Thus if the "weight principle" hold, we must look elsewhere for the structure of protons and neutrons. It is feasable that they could be made of leptons held together by some kind of charge changing force so that they appear on average to have a fractional charge. Their weights would be distorted by this force to give them the apparent weights of the quarks. This is simply one alternative to the quark model - there are others.

    Further it is thought that gravitino fields acting in pairs would consitute the Higgs field. Much like electrons acting in pairs create super-conducing materials.

    The graviton has interaction-weight 0 and so can attach itself to any interaction in any quantities. In fact it is useful if we call the graviton field H to construct a new field G given by

    G=1 + H + H^2/2 + H^3/6 + ... =exp(H)

    Now this is a scalar field and solving its field equations for a symmetric source gives:

    G = 1-2m/r

    We find that this predicts elliptic orbits but no bending of light, which is at odds with current thinking. However, like superstring theory, we cannot alter things as we wish and so if we accept the "weight principle" we would have to re-examine the explanation of the bending of light by the sun. It may be caused by something else besides gravity. (More about gravity modelled as a scalar field can be found at Scalar gravity ).

    The entire action derived from the "weight principle" can be found using 4 dimensions, x, and 8 grassman numbers, G, and is given by:

    Action= Integral{ exp( F(x,G) + GDG ) } dx^4 dG^8

    where F is the superfield, D is the derivative mutiplied by an 8x8 real ant-symmetric dirac matrix. The terms of this expansion gives all those terms consistent with the "weight principle".

    In conclusion I would like to say that the "weight principle" gives a complete theory of particle interactions which because it is related to the power-counting principle of renormalisation is possibly finite. The differences between this and the Standard Model are 2 things:
    1) The structure of protons/neutrons are not made of fractional quarks according to this principle.
    2) Gravity, by this principle, is given by a relativistic scalar field and so no bending of light is predicted as a result of gravity.

    The most interesting aspect of this theory is whether it can be proved to be finite.

    The "weight principle" is calculated with interesting diagrams like Feynamn diagrams except that each vertex has 8-legs. For example 3 legs grouped together represents a fermion and a loop represents a derrivative. Because of the coinindence that the dirac matrices can be written in complex form, the lines can also be given arrows. Each line coming into a vertex is numbered from 1..8 (or 1..4 with arrows) and no two lines coming into a vertex can be given the same number (unless the arrows are opposite). However, the lines change number before going into a different vertex. Since these diagrams all have 8-legs another name for the "weight principle", which I quite like is "Spider-gram Theory".

    Dr Paul Bird

  2. jcsd
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