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Symmetry And Group

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2) 9, = 8 (DD)' I@+('. In terms of component fields the &independent part of -Yo is given by ~ 1 1 1 1 A+*Z'A+ + ~= - l4 A+*PA+ ~ =+ laA+l2 ~ -2 4 2 $+(a - i3)I)++ IF+\*, + $+GI)+ + lF+12 + gradient term. 3) The gradient term can be gathered into the &dependent part and forgotten. Fortachritte der Physlk", Heft 2 i&+ = 0 , P, = 0 , ABDUSSALAMand J. STRATHDEE 90 and their complex conjugates. 3) is that it determines the dimensionality of the fields. Thus, in natural units, [A+]= M , [++I = M3'2.

Their'role here is to provide a "metricyyfor the other fields in the system. C"e-z'J''Q-'@-l. '. 30) is merely a convenience. P in the form of a herniitian matrix. 32) where Rk, I,! , 8, denote the Cell-Mann niatrices. A superfield analogue of the field strengths can be defined. 33) 2 f2 where the nunierical coefficient is chosen for later convenience. This superfield is chiral with respect to both its 0 structure and its spinor index, D-Y++= 0 and (1 - iy5) Y4+= 0 , and so belongs to the transverse vector representations discussed in Section 11, Eq.

Ex+ + 1 - 1 - e-e+/+ + e+e-G+(--iat+). - (coy S D . 59) and the resulting variations of V,, I. 51). C. Parity Conservation Tn this section we wish to prove the important result thot a supersymmetric, renormalizable, fermion-number-conserving Lagrangian theory which also preserves parity must be a gauge theory of a very special form. 13). For a parity operation to be defined, the supermultiplets @+ and 0must be put into correspondence. 62) 9 where w is some unitary matrix subject to the constraint wa = f l .

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