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By Samiou E.

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Although we have illustrated the cancellation of quadratic divergences with just a few examples, it is important to stress that this is a general feature of supersymmetric theories. 7, this cancellation of quadratic divergences occurs to all orders in perturbation theory. 1 Rotations In classical mechanics, rotations of three-vectors can be represented by a rotation matrix R acting upon vectors such as x = (x, y, z) as xi → xi = Ri j x j . 2) where the direction of θ is along the axis about which the rotation occurs, and its magnitude is the rotation angle.

Zumino, Nucl. Phys. B70, 39 (1974). This is not, however, the first paper on (relativistic) spacetime supersymmetry. This distinction belongs to Y. Golfand and E. Likhtman, JETP Lett. 13, 323 (1971) who introduced the supersymmetric extension of the Poincar´e algebra. Motivated by the possibility that the neutrino could be the Goldstone fermion (see Chapter 7) associated with the spontaneous breakdown of a fermionic symmetry, D. Volkov and V. Akulov, JETP Lett. 16, 621 (1972) and Phys. Lett. B46, 109 (1973) independently constructed a model with non-linearly realized supersymmetry.

6) This is the Lagrangian for free fields A, B, and ψ. When these fields obey their respective equations of motion, their quanta correspond to two spin zero particles A and B, and a self-conjugate, spin 12 particle, all with the same mass. Once again, we see that there is an exact match between the bosonic and fermionic degrees of freedom. 2 SUSY transformations and invariance of the action In quantum field theory, a symmetry transformation is a transformation which leaves the equations of motion for the fields of the theory invariant.

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