[doc] background fixes

Author: HugoStrand

doc/background/ppsc.rst

@@ -3,7 +3,7 @@
 A word on the algorithm
 =======================
 
-The hybridization expansion approach to solving generalized Anderson impurity models has been combined with a plethora of numerical methods. One of these methods is the bold hybridization expansion [#ppsc]_ in terms of the local atomic propagator :math`G(\tau)`, often referred to as the pseudo-particle approach, since it can be derived by introducing a pseudo particle for each many-body state in the impurity local Hilbert space.
+The hybridization expansion approach to solving generalized Anderson impurity models has been combined with a plethora of numerical methods. One of these methods is the bold hybridization expansion [#ppscintro]_ in terms of the local atomic propagator :math`G(\tau)`, often referred to as the pseudo-particle approach, since it can be derived by introducing a pseudo particle for each many-body state in the impurity local Hilbert space.
 
 In the bold formulation :math:`G(\tau)` is self-consistently computed using the Dyson equation
 
@@ -15,14 +15,14 @@ where :math:`G_0(\tau)` is the atomic many-body propagator and :math:`\Sigma(\ta
 
 .. math::
 
-   \Sigma[G] = \Sigma_1[G] + \Sigma_2[G] + ... + \Sigma_n[G]
+   \Sigma[G] = \Sigma_1[G] + \Sigma_2[G] + \dots + \Sigma_n[G]
 
-Once convergence is reached physical response functions like the single particle Green's function :math:`g(\tau) = \rangle \mathcal{T} c(\tau) c^\dagger(0) \range` can be evaluted by a separate diagrammatic series (similar to :math:`\Sigma`).
+Once convergence is reached physical response functions like the single particle Green's function :math:`g(\tau) = \rangle \mathcal{T} c(\tau) c^\dagger(0) \rangle` can be evaluted by a separate diagrammatic series (similar to :math:`\Sigma`).
 
-The ``triqs_soehyb`` solver implements the bold hybridization expansion using the Discrete Lehmann Representation (DLR)[#dlr, #cppdlr]_ for compact representation of propagators in imaginary time :math:`\tau` and a separate hybridization function compression approach[#soehyb]_ (based on the famous AAA algorithm) to evaluate the diagram series for :math:`\Sigma` with lower computational complexity than standard quadrature integration.[#dlrhyb]_
+The ``triqs_soehyb`` solver implements the bold hybridization expansion using the Discrete Lehmann Representation (DLR) [#dlr, #cppdlr]_ for compact representation of propagators in imaginary time :math:`\tau` and a separate hybridization function compression approach [#soehyb]_ (based on the famous AAA algorithm) to evaluate the diagram series for :math:`\Sigma` with lower computational complexity than standard quadrature integration. [#dlrhyb]_
 
 
-.. [#ppsc] `M. Eckstein, P. Werner, Phys. Rev. B 82, 115115 (2010) <https://doi.org/10.1103/PhysRevB.82.115115>`_
+.. [#ppscintro] `M. Eckstein, P. Werner, Phys. Rev. B 82, 115115 (2010) <https://doi.org/10.1103/PhysRevB.82.115115>`_
 .. [#dlrhyb] `J. Kaye, Z. Huang, H. U.R. Strand, D. Golež, Phys. Rev. X 14, 031034 (2024) <https://doi.org/10.1103/PhysRevX.14.031034>`_
 .. [#soehyb] `Z. Huang, D. Golež, H. U.R. Strand, J. Kaye, arXiv:2503.19727 (2025) <https://doi.org/10.48550/arXiv.2503.19727>`_
 .. [#cppdlr] `J. Kaye, H. U.R. Strand, N. Wentzell, J. Open Source Softw., 9(100), 6297, (2024) <https://doi.org/10.21105/joss.06297>`_