Add some citations regarding the direct limit.

Overview-paper/Physics.bib

@@ -795,7 +795,39 @@ @book{ashcroft:2005a
 	Publisher = {Harcourt College Publishers},
 	Title = {Solid {S}tate {P}hysics},
 	Year = {1976},
-	Bdsk-Url-1 = {http://www.zentralblatt-math.org/zmath/en/search/?format=complete&q=an:1118.82001}}
+	Bdsk-Url-1 = {http://www.zentralblatt-math.org/zmath/en/search/?format=complete&q=an:1118.82001}}
+
+@Article{ashtekar_representation_1993,
+  author =        {Ashtekar, Abhay and Lewandowski, Jerzy},
+  title =         {Representation {{Theory}} of {{Analytic Holonomy C}}* {{Algebras}}},
+  year =          {1993},
+  month =         nov,
+  archiveprefix = {arXiv},
+  eprint =        {gr-qc/9311010},
+  eprinttype =    {arxiv},
+  keywords =      {General Relativity and Quantum Cosmology,High Energy Physics - Theory,Mathematics - Algebraic Geometry},
+  timestamp =     {2016-06-09T20:19:03Z},
+  urldate =       {2016-06-09}
+}
+
+@Article{ashtekar_representations_1992,
+  author =        {Ashtekar, Abhay and Isham, C. J.},
+  title =         {Representations of the holonomy algebras of gravity and non-{{Abelian}} gauge theories},
+  journal =       {Classical and Quantum Gravity},
+  year =          {1992},
+  volume =        {9},
+  number =        {6},
+  pages =         {1433--1467},
+  month =         jun,
+  archiveprefix = {arXiv},
+  doi =           {10.1088/0264-9381/9/6/004},
+  eprint =        {hep-th/9202053},
+  eprinttype =    {arxiv},
+  issn =          {0264-9381, 1361-6382},
+  keywords =      {High Energy Physics - Theory},
+  timestamp =     {2016-06-09T20:18:50Z},
+  urldate =       {2016-06-09}
+}
 
 @unpublished{aubrun:2010a,
 	Author = {Aubrun, Guillaume and Szarek, Stanis{\l}aw and Werner, Elisabeth},
@@ -3218,6 +3250,25 @@ @unpublished{dittrich_decorated_2014
 	author = {Dittrich, Bianca and Mizera, Sebastian and Steinhaus, Sebastian},
 	year = {2014},
 	note = {arXiv:1409.2407},
+}
+
+@Article{dittrich_discrete_2012,
+  author =        {Dittrich, Bianca},
+  title =         {From the discrete to the continuous - towards a cylindrically consistent dynamics},
+  journal =       {New Journal of Physics},
+  year =          {2012},
+  volume =        {14},
+  number =        {12},
+  pages =         {123004},
+  month =         dec,
+  archiveprefix = {arXiv},
+  doi =           {10.1088/1367-2630/14/12/123004},
+  eprint =        {1205.6127},
+  eprinttype =    {arxiv},
+  issn =          {1367-2630},
+  keywords =      {General Relativity and Quantum Cosmology,High Energy Physics - Lattice,Quantum Physics},
+  timestamp =     {2016-06-06T08:39:55Z},
+  urldate =       {2016-06-06}
 }
 
 @incollection{divincenzo:1998a,

Overview-paper/ymoverview.tex

@@ -819,7 +819,7 @@ \section{The continuum limit}
 
 Conditioned on the validity of the previously mentioned conjectures, we've produced a sequence of states $|\Psi_m\rangle$ which tend, in the limit, to the (lattice) zero-coupling state. The important observation here is that since each term in our sequence is a MERA the correlation length of $|\Psi_m\rangle$ is given by $\xi_m = a_m\lambda^m$, for some $\lambda>0$.  Given that the correlation length $\xi$ of pure Yang-Mills theory is only determined up to a constant which is ultimately fixed by experiment forces us to set the lattice spacing $a_m$ of the state $|\Psi_m\rangle$ to $a_m = a_0\lambda^{-m}$, where $a_0$ is a constant. Thus we have a sequence of states $|\Psi_m\rangle$ for lattices of ever finer discretisation. Each term in the sequence is the result of an isometry applied to a previous term. Further, we can compute all $n$-point functions for this sequence. It turns out that this is enough data to specify a continuum hilbert space and a canonical continuum ground state. 
 
-The continuum hilbert space we describe here is known as a \emph{direct limit} of hilbert spaces; in the context we use it here we call this direct limit the \emph{semicontinuous limit} \footnote{This terminology was suggested to us by Vaughan Jones.} to indicate that it doesn't quite correspond to what we might demand of a full continuous quantum Yang-Mills theory. Note that the direct limit is a basic categorical construction (you can read about it further in, e.g., \cite{lang:2002a}). The application of the direct limit to hilbert spaces has a very long history; one early proposal to use the direct limit to model continuum limits can be found in \cite{bimonte_lattices_1996}, but there are surely prior proposals. A recent fascinating attempt to use the direct limit to build continuum limits of lattice theories, in particular, conformal field theories, can be found in \cite{jones_unitary_2014}.
+The continuum hilbert space we describe here is known as a \emph{direct limit} of hilbert spaces; in the context we use it here we call this direct limit the \emph{semicontinuous limit} \footnote{This terminology was suggested to us by Vaughan Jones.} to indicate that it doesn't quite correspond to what we might demand of a full continuous quantum Yang-Mills theory. Note that the direct limit is a basic categorical construction (you can read about it further in, e.g., \cite{lang:2002a}). The application of the direct limit to hilbert spaces has a very long history; one early proposal to use the direct limit to model continuum limits can be found in \cite{bimonte_lattices_1996}, but there are surely prior proposals. It is, for example, a standard technique in quantum gravity \cite{ashtekar_representations_1992, ashtekar_representation_1993, dittrich_discrete_2012}. A recent fascinating attempt to use the direct limit to build continuum limits of lattice theories, in particular, conformal field theories, can be found in \cite{jones_unitary_2014}.
 
 Let $\mathcal{D}$ be the directed set of regular partitions of $\mathbb{R}^d$ induced by integer lattices with lattice spacing $a$, i.e., $a\mathbb{Z}^d$. This set is directed by \emph{refinement}, i.e., a partition $Q$ is a \emph{refinement} of $P$, denoted $P \preceq Q$, if every element of $Q$ is a subset of an element of $P$. (A useful mnemonic to remember the ordering is that $Q$ has ``more'' elements than $P$.) We regard every lattice spacing $a$ as giving rise to a \emph{physically different} lattice.