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Quantum field theory of many-body systems

Xiao-Gang Wen

His web page

http://dao.mit.edu/~wen/

I thought that his book might be easier than his papers. hehehe It's a text book.

I did get to learn a few things.

Here is what wiki says about the subject.

In physics, topological order is a new kind of order (a new kind of organization of particles) in a quantum state that is beyond the Landau symmetry-breaking description.

http://en.wikipedia.org/wiki/Topological_order

Why is topological order important? Landau symmetry-breaking theory is a cornerstone of condensed matter physics. It is used to define the territory of condensed matter research. The existence of topological order appears to indicate that nature is much richer than Landau symmetry-breaking theory has so far indicated. The exciting time of condensed matter physics is still ahead of us. Some suggest that topological order (or more precisely, string-net condensation) has a potential to provide a unified origin for photons, electrons and other elementary particles in our universe.

http://en.wikipedia.org/wiki/String-net_condensation

For strings labeled by the positive integers, string-nets are the spin networks studied in loop quantum gravity. This has led to the proposal by Wen and Levin, [1] , and Smolin, Markopolou and Tomasz, [2] that loop quantum gravity's spin networks can give rise to the standard model of particle physics through this mechanism, along with fermi statistics and gauge interactions.

**To date, a rigorous derivation from LQG's spin networks to Wen's spin lattice has yet to be done.**

I found the following trying to make the relationship with LQG

http://arxiv.org/abs/hep-th/0611197

Quantum Graphity

Tomasz Konopka, Fotini Markopoulou, Lee Smolin

(Submitted on 17 Nov 2006) )

“We argue (but do not prove) that under certain conditions the spins in the system can arrange themselves in regular, lattice-like patterns at low temperatures. When the graph is frozen, the model is closely related to a model of Levin and Wen [4, 5, 6] which has emergent gauge degrees of freedom.”

p.7

“…it is helpful to first consider the graph of “on” links to be frozen in a particular configuration, say a regular cubic lattice where the minimal loops in the graph are plaquettes. In this case, these terms reduce to the rotor model of Levin and Wen [6]”

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Xiao-Gang Wen ends his book with the following:

“What is the origin of gauge field – geometrical or dynamical?

What is the origin of Fermi statistics – given or emergent?

In this book, we favor the dynamical and emergent origin of gauge bosons and fermions. The gauge bosons and the Fermi statistics may just be collective phenomena of quantum many-boson systems, and nothing more.”

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Has anyone got any other link that try to make the relationship with LQG?

jal