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By B. Renner, D. ter Haar

ISBN-10: 0080033725

ISBN-13: 9780080033723

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7) and neglecting the form factors Gf,PN and Gf,pN because the contribu­ tion of their kinematic forms is of the order (mP — mN), and for the same reason neglecting the dependence of GftPN on the momen­ tum transfer. 18. gA is the quotient of the measured axial and vector coupling constants in ß decay. 35) In the neutron term we sum over the spin and obtain Σ ûp{p)ybyQuN{p)ûN(p)yhyQUp{p) pol = üP(p)y5y0(ypN + mN)y5y0Up(p) = up{p)yQ{ypN-mN)yQUp(p) üp{p){y(ßN+yp-mN)up(p) = = 2üp (p) (yp)up(P) 0 n the approximation mN=mP ^>EN=EP) = 4 £ 2 ^ 1 -(f) 2 )· <2·36> In the continuum we introduce the divergences D(±) = θ (7μ±(/μ) and integrate over all internal degrees of freedom of the intermediate states, leaving only the integration over the total mass to be done.

4. Lepton Scattering Sum Rules The most direct way of testing a commutator is the insertion of a complete set of intermediate states into its matrix elements. 29) we obtain the sum rule tNumbered references under Bibliography on Current Algebra at end of book. ÌRecent contributions: (422), (456), (463). 30) <β|β*Ι*> = /(Λτ)»<β|Λ(ατ)|6> = j {dxY exp i(pa~pb)x . ò*(p°-p»)(a\j*(0)\b). 32) where Σ' denotes a restricted summation: only over states with equal spatial momentum. 32) will be called direct sum rules.

The symmetry limit of the algebra would require massless hadrons;(166) this does not seem to be a good approximation to strong interaction physics. Of the generators Q\ Q\ Q\ Q\ ß 3 + (1/V3) ß 8 ; ß 1 , Q\ Q\ 5 ß are directly observable in electromagnetic and weak reactions; in the limit of isospin symmetry we can construct ß 6 , ß 7 , ß 3 , ß 6 , ß 7 and also separate ß 3 from ß 8 ; ß 8 is directly accessible only in the SU3 symmetry limit. It is not known whether there is any deeper significance behind this distinction.

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Current Algebras and their Applications by B. Renner, D. ter Haar

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