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You could get an idea if the spectra are the same with the possible exception of the ground state. That would require a lot of work to diagonalize theoretically but is more experimental. That is a first check. You then have to find find an $a$ that annihilates the ground state. Then get a factorization of the Hamiltonian.


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He inserts the identity $I = \sum_{S'}|S'\rangle\langle S'|$. This gives $\langle S|Q_\alpha Q_\alpha^\dagger|S\rangle = \sum_{S'} \langle S|Q_\alpha |S'\rangle \langle S'|Q_\alpha^\dagger|S\rangle =\sum_{S'} |\langle S|Q_\alpha |S'\rangle|^2 $.


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Yes. OP is right. There is a minus. Since by convention the complex conjugation obeys $$ (z w)^{\ast} ~=~ w^{\ast}z^{\ast}~=~(-1)^{|z|~|w|} z^{\ast}w^{\ast} \tag{1}$$ for any two supernumbers $z$, $w$ (of definite Grassmann parities $|z|$,$|w|$), we should also have $$ (A f)^{\ast} ~=~(-1)^{|A| ~|f|} A^{\ast}f^{\ast} \tag{2}$$ for an operator $A$ and ...


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I have talked with people more knowledgeable than I on SUSY, and they agree that something isn't right here. I'm posting my correction to the above in case someone has this problem in the future. This is missing from the errata. We start with (2.60) $$\mathcal{L}=-\frac{1}{2}W^{jk}\psi^{\alpha}_{j}\psi_{\alpha k} + W^{j}F_{j} +h.c.$$ We have the following ...


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Eq. (4.4.11g) is for a Majorana spinor SUSY charges $Q_a$, $a=1,2,3,4$, while eq. (3.1.31) is for left Weyl spinor SUSY charges $Q_{\alpha}$, $\alpha=1,2$.


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Normally the notation $(n_b|n_f)$ denotes the dimension of a super vector space of Grassmann-even dimension $n_b$ and Grassmann-odd dimension $n_f$. When writing a super vector as a column vector, it is standard to order the Grassmann-even sector before the Grassmann-odd sector. However, the authors introduce a non-standard ordering $(n_{b_1}|n_f|n_{b_2})$ ...


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the big bang created the real space vacum when the "explotion" created a "super Situation" the expantion is faster then light and will create a vacum "inside" and push the event horrizon away and back in the same action


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(Answering rather than commenting for lack of rep). My focus is in programming however perhaps the following would help (From what I can understand due to different terminology): Instead of reducing the components, how about factoring them into higher dimensions, I imagine the irregularities would become more apparent given the supposed symmetrical outcome, ...


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In the Standard Model coupled to GR as an effective theory, the cosmological constant is predicted to be $m_{Pl}^4$ i.e. $10^{123}$ times the correct value (you mentioned the correct value). SUSY improves this situation by cancellations between superpartners (fermions contribute the same to the C.C. as their bosonic partners but with the opposite sign if ...


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this question is 2 years old, but I thought it's never too late. I'm not sure about the definite answer, but here are my thoughts. Take the SO(6) algebra viewpoint. The $\mathbf{6}$ is the fundamental (vector) representation, and the $\mathbf{4}$ is the spinor representation. So we are looking for symbols $\Sigma_{AB}^I$ that combine two spinors into a ...



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