From 08a3858e27a6e52fec9d268f23a6d5599461238b Mon Sep 17 00:00:00 2001 From: Jacob Beyer <beyer@physik.rwth-aachen.de> Date: Fri, 15 Sep 2023 12:53:29 +0200 Subject: [PATCH] Some small fixes --- main.tex | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/main.tex b/main.tex index 7871875..f377c3b 100644 --- a/main.tex +++ b/main.tex @@ -44,7 +44,7 @@ superscriptaddress, floatfix, longbibliography]{revtex4-2} \node[shape=circle,draw,inner sep=1pt] (char) {#1};}} \MakeRobustCommand\circled -\newcommand{\su}{SU} +\newcommand{\su}{SU(2)~} \newcommand{\bvec}[1]{\boldsymbol #1} \newcommand{\Ucrit}{U_\mathrm{c}} @@ -252,7 +252,7 @@ Thorough derivations of the FRG equations can be found in Refs.\,\onlinecite{metzner2012,dupuis2021,platt2013,beyer2022a} among others, here we only give the briefest overview of our chosen approximations: -The diagrammatic representation of our single-loop, non-$SU(2)$ flow-equation +The diagrammatic representation of our single-loop, non-\su flow-equation is given in \cref{fig:diags}. During the calculation we neglect higher loop orders, the flow equations for the self-energy $\frac{\dd}{\dd\Lambda}\Gamma^{(2)}$ as well as the @@ -289,7 +289,11 @@ we determine. The second important property is the state's total irreducible representation (irrep), which must be equal in both spin spaces\,\cite{sigrist1987}. This can be obtained from the simulated momentum's irrep in conjunction with -the respective spin's irrep. +the respective spin's irrep, in accordance with the eigenstate's product +decomposition +\begin{equation} + v = \Psi \otimes \Delta_{\Psi}(\bvec k) + \bvec d \otimes \Delta_{\bvec d}(\bvec k) +\end{equation} A careful symmetry analysis in conjunction with the possible combinations is presented in the following. -- GitLab