โ Scribed by Ali H Chamseddine
No coin nor oath required. For personal study only.
We construct a Lagrangian density which is manifestly invariant under the orthosymplectic gauge group OSP(l; 4) and under general coordinate transformations. This is done by the use of two multiplets, the symmetric and antisymmetric representations of OSP(l; 4). We present the general features of OSP(m; 2n) and, in particular, its irreducible representations. The absence of OSP(1; 4) symmetry from the ground state indicates that one of the scalar fields, which is an element of the symmetric multiplet, has a nonvanishing vacuum expectation value. A shift in the fields reveals the physical spectrum of our Lagrangian. Two Goldstone fields are present, a vector and a spinor, corresponding to the breakdown of OSP(1; 4) to the Lorentzian group. The full Lagrangian contains a graviton, a massive spin-$ field, and two massive scalar fields. The generalization to OSP(2; 4) is immediate.
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