WIP infinite sys.

Former-commit-id: e14d9ee7a04af1fa42b2a7de849de0569a2eb471

lepaper/finite.lyx

@@ -968,6 +968,13 @@ reference "eq:plane wave expansion"
 
 \begin_layout Subsection
 Multiple scattering
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Multiple-scattering"
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard

lepaper/infinite.lyx

@@ -95,6 +95,16 @@
 
 \begin_layout Section
 Infinite periodic systems
+\begin_inset FormulaMacro
+\newcommand{\dlv}{\vect b}
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\rlv}{\vect b}
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
@@ -121,13 +131,43 @@ Topology anoyne?
  scatterer arrays.
 \end_layout
 
+\begin_layout Subsection
+Notation
+\end_layout
+
 \begin_layout Subsection
 Formulation of the problem
 \end_layout
 
 \begin_layout Standard
-Assume a system of compact EM scatterers in otherwise homogeneous and isotropic
- medium, and assume that the system, i.e.
+Let us have a linear system of compact EM scatterers on a homogeneous background
+ as in Section 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "subsec:Multiple-scattering"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+, but this time, system shall be periodic: let there be a 
+\begin_inset Formula $d$
+\end_inset
+
+-dimensional (
+\begin_inset Formula $d$
+\end_inset
+
+ can be 1, 2 or 3) lattice embedded into the three-dimensional real space,
+ with lattice vectors.
+ set of 
+\begin_inset Formula $d$
+\end_inset
+
+ (one to three) lattice vectorsAssume a system of compact EM scatterers
+ in otherwise homogeneous and isotropic medium, and assume that the system,
+ i.e.
  both the medium and the scatterers, have linear response.
  A scattering problem in such system can be written as
 \begin_inset Formula 
@@ -295,7 +335,7 @@ reference "eq:W definition"
 
  in terms of integral with a delta comb
 \begin_inset FormulaMacro
-\newcommand{\basis}[1]{\mathfrak{#1}}
+\renewcommand{\basis}[1]{\mathfrak{#1}}
 \end_inset