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# SOSpin, a C++ library for Yukawa decomposition in SO(2N) models SOSpin (one reads it as a single word “sospin”) is a C++ Library whose purpose is to decompose Yukawa couplings invariant under SO(2N) groups in terms of the SU(N) degrees of freedom subgroup. We include specific functions to address the SO(10) case.

How to write the spinorial SO(2N) representation in terms of SU(N) states?
Answer: The Link - annihilation and creation operators - $b_i$ and $b^\dagger_i$ ! The description via wave functions is substituted by the use of creation, $\color{blue} b^{\dagger}_i$, and annihilation, $\color{blue}b^{}_i$, operators: \begin{equation*} \Psi\longrightarrow|\Psi\rangle=|0\rangle\psi \,+\,b^{\dagger}_i|0\rangle\psi^i \,+\, \frac{1}{2}\psi^{ij} \, b^{\dagger}_i b^{\dagger}_j|0\rangle \,+\, \cdots +\, \frac{1}{N!} \varepsilon^{ij\cdots k}\, \underbrace{b^{\dagger}_i b^{\dagger}_j\cdots b^{\dagger}_k}_N |0\rangle\bar{\psi} \end{equation*} Grassmann Algebra: $\{b_i,b^{\dagger}_j\}=\delta_{ij}\,\quad\text{and}\quad\{b_i,b_j\}=0=\{b^{\dagger}_i,b^{\dagger}_j\}$.

More details describing the formalism can be found in the manual.

## Publication

If you use this code or parts of it, please cite the paper:

1. Nuno Cardoso, David Emmanuel-Costa, Nuno Gonçalves, C. Simões, "SOSpin, a C++ library for Yukawa decomposition in SO(2N) models", arXiv:1509.00433, 2015.