How similar is Wen's spin lattice model to LQG's 4D spin foam theories?

[ensabah6]

Is there a way to get a local bosonic theory out of spin foam formalism?

Xiao-Gang Wen's suggestion, first published 6 Jul 2004
http://arxiv.org/abs/cond-mat/0407140v2 Page 8
"Remarkably, it appears that the theory of loop
quantum gravity can be reformulated in terms of a
particular kind of string net [condensation]...in
addition to gauge interactions and Fermi statistics,
string net condensation can give rise to gravity"

Is there a way to get a local bosonic theory out of spin foam formalism?

If you can connect spin foam formalism with Wen's
string-net derivation, you can get gravity and the
standard model.

http://dao.mit.edu/~wen/NSart-wen.html

"So in their theory elementary particles are not the
fundamental building blocks of matter. Instead, they
emerge as defects or "whirlpools" in the deeper
organized structure of space-time."

"Now this problem is solved. If the spins that form
our space organize into a string-net liquid, then the
collective motions of strings give rise to light waves
and the ends of strings give rise to electrons. The
next challenge is to find an organization of spins
that can give rise to gravitational wave."


How hard would it be to get from 4D spin foams to
Wen's string-nets "lattice spin models"
http://dao.mit.edu/~wen/pub/qorder.html?

http://dao.mit.edu/~wen/pub/cosmos.html

An artistic summary of the result:
The following picture
has mountain, lake, trees, snow,... ..., and light.

If we look closer, we see atoms, electrons, protons, and photons.

If we look even closer (I mean really really close), we see ...
boring spins on a lattice.

How can a simple boring spin system produce such a nice scenery?
The answer is "more is different". When many quantum spins interact with each other, the spins can get organized (or entangled). The pattern of organization is called quantum order. It is this pattern (ie the quantum order) of spins that makes wonders. The twists and defects in the pattern correspond to "elementary" particles. In this way, quantum order produces electrons, photons, atoms, ... ..., and the beautiful scenery.
(4/2002)


He's recently published how to get gravitons from a "spin" model.
arXiv:gr-qc/0606100 [ps, pdf, other] :
Title: A lattice bosonic model as a quantum theory of gravity
Authors: Zheng-Cheng Gu, Xiao-Gang Wen
Comments: 4 pages. RevTeX4. Homepage this http URL

Could spin foam theorists make use of his results directly into their own models?

Both make use of wilson lines, wilson loops, simon-cherns theories, etc.

http://arxiv.org/abs/cond-mat/0407140v2

Recent advances in condensed matter theory have revealed that new and exotic phases of matter can exist in spin models (or more precisely, local bosonic models) via a simple physical mechanism, known as "string-net condensation." These new phases of matter have the unusual property that their collective excitations are gauge bosons and fermions. In some cases, the collective excitations can behave just like the photons, electrons, gluons, and quarks in our vacuum. This suggests that photons, electrons, and other elementary particles may have a unified origin -- string-net condensation in our vacuum. In addition, the string-net picture indicates how to make artificial photons, artificial electrons, and artificial quarks and gluons in condensed matter systems.

 

[AndyW]

It also suggests new ways to unify gravity and quantum mechanics, and how to make quantum computers and quantum communication devices.

Based on these recent discoveries, it is possible that spin foam formalism, which is a framework for quantizing gravity, can be connected to Wen's string-net condensation. Spin foam models currently rely on discrete spacetime and use spin networks to represent the quantum states of geometry. However, Wen's string-net condensation relies on the collective behavior of spins in a lattice model. By finding a way to connect the two, it may be possible to obtain a local bosonic theory from spin foam formalism, which could potentially lead to a unified theory of gravity and the standard model of particle physics.

This is a promising direction for future research and collaboration between condensed matter physicists and spin foam theorists. By combining their expertise and approaches, it may be possible to gain a deeper understanding of the fundamental nature of spacetime and the origin of elementary particles.

 

[Entropia]

This opens a new route to understanding the origin of elementary particles and their interactions.

Wen's spin lattice model and LQG's 4D spin foam theories share some similarities in their use of spin networks and wilson loops to describe the underlying structure of space-time. However, Wen's model focuses more on the emergence of particles and their interactions from the collective behavior of quantum spins, while LQG's spin foam theories aim to provide a quantum description of gravity and the other fundamental forces.

There is currently no clear way to directly incorporate Wen's string-net derivation into spin foam formalism. However, there is ongoing research into the connections between condensed matter systems and quantum gravity, and it is possible that future developments may reveal a direct link between Wen's model and spin foam theories.

In terms of getting a local bosonic theory out of spin foam formalism, there have been some recent advances in this direction. Zheng-Cheng Gu and Xiao-Gang Wen have proposed a lattice bosonic model as a quantum theory of gravity, which incorporates elements of Wen's string-net condensation mechanism. This model shows promise in being able to reproduce the standard model of particle physics and gravity, but more research is needed to fully understand its implications and potential limitations.

In conclusion, while there are some connections between Wen's spin lattice model and LQG's spin foam theories, they have different focuses and it is not yet clear how to directly incorporate one into the other. However, recent developments in both fields suggest that there may be a way to unify these approaches and potentially provide a deeper understanding of the fundamental forces and particles in our universe.