ncg

commit fd580db32388d4d35d9c95c07828b876a69cdaa5
parent f8c6751f8899b6c9731587ca3c63830852f52f7d
Author: miksa234 <milutin@popovic.xyz>
Date:   Fri, 23 Jul 2021 13:07:43 +0200

small checkpoint fix in heatkernel

Diffstat:
M
src/thesis/chapters/electroncg.tex
 | 
2
+-
M
src/thesis/chapters/heatkernel.tex
 | 
8
+++++---
M
src/thesis/main.pdf
 | 
0

3 files changed, 6 insertions(+), 4 deletions(-)
diff --git a/src/thesis/chapters/electroncg.tex b/src/thesis/chapters/electroncg.tex
@@ -402,7 +402,7 @@ for a $\xi \in H^+$. Then the straight forward calculation gives \begin{align}
         D_F)\tilde{\xi})\label{eq:fermionic3},
 \end{align}
 (note that we add the constant $\frac{1}{2}$ to the action).
-For the term in \ref{fermionic:1} we calculate
+For the term in \ref{eq:fermionic1} we calculate
 \begin{align}
     \frac{1}{2}(J\tilde{\xi}, (D_M\otimes 1)\tilde{\xi}) &=
     \frac{1}{2}(J_M\tilde{\chi}_R,D_M\tilde{\psi}_L)+
diff --git a/src/thesis/chapters/heatkernel.tex b/src/thesis/chapters/heatkernel.tex
@@ -1,16 +1,18 @@
 \subsection{Heat Kernel Expansion}
 \subsubsection{The Heat Kernel}
 The heat kernel $K(t; x, y; D)$ is the fundamental solution of the heat
-equation. It depends on the operator $D$ of Laplacian type.
+equation
 \begin{align}
-    (\partial _t + D_x)K(t;x, y;D) =0
+    (\partial _t + D_x)K(t;x, y;D) =0,
 \end{align}
+which depends on the operator $D$ of Laplacian type.
+
 For a flat manifold $M = \mathbb{R}^n$ and $D = D_0 := -\Delta_\mu\Delta^\mu +m^2$ the
 Laplacian with a mass term and the initial condition
 \begin{align}
     K(0;x,y;D) = \delta(x,y),
 \end{align}
-takes to form of the standard fundamental solution
+takes the form of the standard fundamental solution
 \begin{align}\label{eq:standard}
     K(t;x,y;D_0) = (4\pi t)^{-n/2}\exp\left(-\frac{(x-y)^2}{4t}-tm^2\right).
 \end{align}
diff --git a/src/thesis/main.pdf b/src/thesis/main.pdf
Binary files differ.