Using Regge high energy behavior, the chiral algebra of charges, and pion pole dominance of the divergence of the axial-vector current, all the strong interaction sum rules which hold for elastic pion-hadron scattering amplitudes at t=O are derived. These include charge algebra sum rules as well as superconvergence relations. We distinguish between \"pure\" t==O sum rules (Class I) and \"extrapolated\" sum rules (Class 11) and relate them to the evenness or oddness of the helicity flip in the t-channel. Using the explicit crossing relations for the relevant helicity amplitudes, the connection of Class I superconvergence relations to the charge algebra sum rules is established, and the algebraic structure of Class I sum rules is then discussed in terms of representations of the SU(2) X SU(2) chiral algebra of charges, for particle states moving with infinite momentum. The properties of the mass operator in SU(2) X SU(2) are analyzed and it is shown that even in the presence of SU(2) X SU(2) symmetry breaking the (mass)' values of all the (mixed) eigenstates of an irreducible representation of the algebra are predicted to be equal, Since these eigenstates can be determined from the matrix elements of the vector and axial-vector charges, a large number of non-trivial mass relations are obtained. Class II superconvergence relations, sum rules for t#O, and sum rules for the derivative with respect to t of the scattering amplitude at t--O are briefly discussed. Many applications of the strong interaction sum rules are presented including a model consisting of I=0 and I=1 scalar, pseudoscalar, vector, and axial-vector mesons. The predictions of the model as well as those of the other sum rules are derived and found to be in satisfactory agreement with experiment.

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Strong-interaction sum rules for pion--hadron scattering.

A review is given of recent applications of symmetry arguments in particle physics. It deals with the developments which start with $\mathrm{SU}(6)$.

Dynamical Symmetry in Particle Physics

This is a PhD thesis written in 2015 as part of a degree within the University of Waterloo.

Standard model physics from an algebra

Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra

We demonstrate a model which captures certain attractive features of SU(5) theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras $$\mathbb {R}$$
 , $$\mathbb {C}$$
 , $$\mathbb {H}$$
 , and $$\mathbb {O}$$
 . From the SU(n) symmetry of these ladder operators, we then demonstrate a model which has much structural similarity to Georgi and Glashow’s SU(5) grand unified theory. However, in this case, the transitions leading to proton decay are expected to be blocked, given that they coincide with presumably forbidden transformations which would incorrectly mix distinct algebraic actions. As a result, we find that we are left with $$G_{sm} = SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb {Z}_6$$
 . Finally, we point out that if U(n) ladder symmetries are used in place of SU(n), it may then be possible to find this same $$G_{sm}=SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb {Z}_6$$
 , together with an extra $$U(1)_X$$
 symmetry, related to $$B\!-\!L$$
 .

/pdf/su-3-c-times-su-2-l-times-u-1-y-left-times-u-1-x-right-s-u-3-23kkdi8st7.pdf

$$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right) $$ S U ( 3 ) C × S U ( 2 ) L × U ( 1 ) Y × U ( 1 ) X as a symmetry of division algebraic ladder operators

Quantized Grassmann variables and unified theories

SU6 and non leptonic hyperon decays

Approximate saturation of superconvergence relation

Theoretical model for π+ N → N +η+η

di Fisiea s - Sezione di Roma R. CASALBVONI (*), L. LVSAN~A and E. SORAC~ Istituto Nazionale di Pisica s - Sezione di ~irenze ricevuto il 22 Aprile 1977)

F. Buccella

Papers

Quantized Grassmann variables and unified theories

SU6 and non leptonic hyperon decays

Approximate saturation of superconvergence relation

Theoretical model for π+ N → N +η+η

Fermi oscillators for vectorlike unified theories with unitary groups