From 5d858bfbebffc411a7baffa06abbcfc52bae6771 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= <marek@necada.org>
Date: Sat, 27 Jul 2019 20:04:56 +0300
Subject: [PATCH] Incremental progress

Former-commit-id: 408ece59a0ed37e6bcbe0cac8c527430a8a2f4d2
---
 lepaper/arrayscat.lyx |  5 +++++
 lepaper/finite-cs.lyx | 40 ++++++++++++++++++++++++++++++++++++++--
 2 files changed, 43 insertions(+), 2 deletions(-)

diff --git a/lepaper/arrayscat.lyx b/lepaper/arrayscat.lyx
index 8a14e90..f858478 100644
--- a/lepaper/arrayscat.lyx
+++ b/lepaper/arrayscat.lyx
@@ -264,6 +264,11 @@
 \end_inset
 
 
+\begin_inset FormulaMacro
+\newcommand{\rcoeffincp}[1]{a_{#1}^{\mathrm{inc.}}}
+\end_inset
+
+
 \begin_inset FormulaMacro
 \newcommand{\rcoeffptlm}[4]{\rcoeffp{#1}_{#2#3#4}}
 \end_inset
diff --git a/lepaper/finite-cs.lyx b/lepaper/finite-cs.lyx
index 8f70501..834bbd3 100644
--- a/lepaper/finite-cs.lyx
+++ b/lepaper/finite-cs.lyx
@@ -395,7 +395,11 @@ todo different notation for the complex conjugation without transposition???
 \end_inset
 
  or in the per-particle matrix notation, 
-\begin_inset Formula $\troprp qp^{-1}=\troprp pq=\troprp qp^{\dagger}$
+\begin_inset Formula 
+\begin{equation}
+\troprp qp^{-1}=\troprp pq=\troprp qp^{\dagger}\label{eq:regular translation unitarity}
+\end{equation}
+
 \end_inset
 
 .
@@ -416,7 +420,11 @@ better wording
 \end_inset
 
 , 
-\begin_inset Formula $\troprp ac=\troprp ab\troprp bc$
+\begin_inset Formula 
+\begin{equation}
+\troprp ac=\troprp ab\troprp bc\label{eq:regular translation composition}
+\end{equation}
+
 \end_inset
 
  but truncation breaks this, 
@@ -624,7 +632,35 @@ noprefix "false"
 
 \end_inset
 
+Using the unitarity 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:regular translation unitarity"
+plural "false"
+caps "false"
+noprefix "false"
 
+\end_inset
+
+ and composition 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:regular translation composition"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+ properties, one has
+\begin_inset Formula 
+\[
+\rcoeffp{\square}^{\dagger}\outcoeffp{\square}=\rcoeffincp p^{\dagger}\sum_{q\in\mathcal{P}}\troprp pqf_{q}.
+\]
+
+\end_inset
+
+ 
 \end_layout
 
 \end_body