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The Lorentz group $O(3,1)$ has spinor representations (actually $SL(2,\mathbb C)$, that is the universal cover of $O(3,1)$), as well known. The problem is that now, in general relativity, we want to deal with generic transformations. So we are working with G$L(4)$. Roughly speaking, the associated Lie Algebra $\mathfrak{gl}(4)$ doesn't admit spinor ...


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For Supersymmetry: -Introduction to Supersymmetry, (Müller-Kirsten, Wiedemann) It's very detailed in every aspect, from graded algebras to the lagrangian of Supersymmetry and symmetry breaking.To be supplemented with something on phenomenology (see below) -Supersymmetry and Supergravity, (Wess, Bagger) Very advanced, but a bit obscure. To be ...


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In the Standard Model, the natural scale for the dimension-two Higgs coupling, $m_H^2$, is the Planck scale, because it takes radiative corrections $\delta M_H^2 \sim M_P^2$. The $\mu$-parameter in the MSSM (or any softly-broken SUSY theory), however, is protected from quadratic divergences by supersymmetry (see the non-renormalization theorem). There is ...


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Lorentz spinors appear as irreducible representations of the group SL(2,C). Elements of the group are 2x2 matrices with complex entries and unity determinant. A Lorentz spinor is a two component vector $\psi^{A},\chi^{A}\in V_{2}$ with $A=1,2$. The Levi-Civita tensor $\epsilon_{AB}$ is an invariant tensor under SL(2,C). This means that if we have an irrep ...


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The matrices $\sigma^{\mu}$, being hermitian, satisfy:$(\sigma^{\mu}_{\alpha\dot{\beta}})^{*}$=$( \sigma^{\mu *})_{\dot{\alpha}\beta}$=$(\sigma^{\mu\dagger})_{\beta\dot{\alpha}}$=$(\sigma^{\mu})_{\beta\dot{\alpha}}$. So $(\xi\sigma^{\mu}\bar\psi)^{*}$=$(\xi^{\alpha}\sigma^{\mu}$$_{\alpha\dot{\beta}}$$\bar{\psi}$$^{\dot{\beta}})$$^{*}$=$\dots$, the rest ...



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