-#LyX 1.6.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 345
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
\begin_document
\begin_header
\textclass aastex
\shortauthors{Collapsed Cores in Globular Clusters}
\end_preamble
\use_default_options false
+\maintain_unincluded_children false
\language english
+\language_package default
\inputencoding default
+\fontencoding global
\font_roman default
\font_sans default
\font_typewriter default
\font_default_family default
+\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
+
\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\use_geometry false
\use_amsmath 0
\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
\cite_engine basic
\use_bibtopic false
+\use_indices false
\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
-\defskip medskip
+\paragraph_indentation default
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
-\author ""
-\author ""
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
\end_header
\begin_body
\end_inset
collisions can be expressed in terms of fermion strings of the form
-\begin_inset Formula \begin{equation}
-\bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),\end{equation}
+\begin_inset Formula
+\begin{equation}
+\bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),
+\end{equation}
\end_inset
\end_inset
and the unit matrix 1 as
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
\gamma^{\mu} & = & \left(\begin{array}{cc}
0 & \sigma_{+}^{\mu}\\
-\sigma_{-}^{\mu} & 0\end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
+\sigma_{-}^{\mu} & 0
+\end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
-1 & 0\\
-0 & 1\end{array}\right),\\
-\sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),\end{eqnarray*}
+0 & 1
+\end{array}\right),\\
+\sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
+\end{eqnarray*}
\end_inset
giving
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\hat{a}=\left(\begin{array}{cc}
0 & (\hat{a})_{+}\\
-(\hat{a})_{-} & 0\end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},\end{equation}
+(\hat{a})_{-} & 0
+\end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},
+\end{equation}
\end_inset
The spinors are expressed in terms of two-component Weyl spinors as
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
u=\left(\begin{array}{c}
(u)_{-}\\
-(u)_{+}\end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.\end{equation}
+(u)_{+}
+\end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.
+\end{equation}
\end_inset
\end_layout
\begin_layout MathLetters
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula
+\begin{eqnarray}
u(p,\lambda)_{\pm} & = & (E\pm\lambda|{\textbf{p}}|)^{1/2}\chi_{\lambda}(p),\\
-v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)\end{eqnarray}
+v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)
+\end{eqnarray}
\end_inset
\begin_layout Standard
Consider a task that computes profile parameters for a modified Lorentzian
of the form
-\begin_inset Formula \begin{equation}
-I=\frac{1}{1+d_{1}^{P(1+d_{2})}}\end{equation}
+\begin_inset Formula
+\begin{equation}
+I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
+\end{equation}
\end_inset
where
-\begin_inset Formula \[
+\begin_inset Formula
+\[
d_{1}=\sqrt{\left(\begin{array}{c}
\frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
-\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}\]
+\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
+\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
d_{2}=\sqrt{\left(\begin{array}{c}
\frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
-\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}\]
+\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
+\]
\end_inset
-\begin_inset Formula \[
-x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\]
+\begin_inset Formula
+\[
+x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
+\]
\end_inset
-\begin_inset Formula \[
-y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta\]
+\begin_inset Formula
+\[
+y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
+\]
\end_inset
\begin_layout Standard
Consider once again a task that computes profile parameters for a modified
Lorentzian of the form
-\begin_inset Formula \begin{equation}
-I=\frac{1}{1+d_{1}^{P(1+d_{2})}}\end{equation}
+\begin_inset Formula
+\begin{equation}
+I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
+\end{equation}
\end_inset
\end_layout
\begin_layout MathLetters
-\begin_inset Formula \[
+\begin_inset Formula
+\[
d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
\frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
-\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}\]
+\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
+\]
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
\frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
-\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}\end{equation}
+\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
+\end{equation}
\end_inset
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula
+\begin{eqnarray}
x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
-y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta\end{eqnarray}
+y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
+\end{eqnarray}
\end_inset
\begin_layout Standard
For completeness, here is one last equation.
-\begin_inset Formula \begin{equation}
-e=mc^{2}\end{equation}
+\begin_inset Formula
+\begin{equation}
+e=mc^{2}
+\end{equation}
\end_inset
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="13">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="right" valignment="top" width="0pt">
<column alignment="right" valignment="top" width="0pt">
projects / lyx.git / blobdiff