What do you think of this definition of Spin Networks?

In summary, the conversation discusses a paper that defines spin networks and their relationship to Hilbert spaces and representations. The author also mentions a specific type of spin network with only one node.
  • #1
Heidi
418
40
Hi Pfs
i found a paper:
https://arxiv.org/abs/math-ph/0306059
in which the author gives a definition of spin networks
it is at the bottom of page 5
the words node or vertex does not appear.
what do you think of it?
Does the author think that all the information is in the hilbert spaces on which the representations act?
 
Last edited:
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  • #2
I read the paragraph too fast. the author said that what followed concerned
the case of r loops passing all through a single node (look a fig 1)
 
  • #3
I understand why. He only considers loops based on a single point . He constrcts then a peculiar spin network with only on node.
 

FAQ: What do you think of this definition of Spin Networks?

What are Spin Networks?

Spin networks are mathematical structures used in theoretical physics, particularly in quantum gravity, to describe the quantum state of the geometry of space. They consist of graphs with edges and vertices, where edges are labeled by spins (representations of the SU(2) group), and vertices represent the intertwining of these spins.

How do Spin Networks relate to Loop Quantum Gravity?

In Loop Quantum Gravity (LQG), spin networks provide a basis for the quantum states of the gravitational field. They represent the quantized geometry of space, where the nodes and links of the network correspond to quantized volumes and areas, respectively.

What is the significance of spins in Spin Networks?

Spins in spin networks correspond to the irreducible representations of the SU(2) group, which is related to angular momentum in quantum mechanics. These spins determine the geometric properties of space at the quantum level, such as the quantized areas of surfaces intersected by the network's edges.

How do Spin Networks evolve over time?

In the context of quantum gravity, the evolution of spin networks is described by spin foams, which are higher-dimensional analogs of spin networks. Spin foams represent the history of spin networks over time, providing a framework for understanding the dynamics of quantum spacetime.

What are the applications of Spin Networks beyond quantum gravity?

While spin networks are primarily used in the study of quantum gravity, they also have applications in other areas of physics and mathematics, such as topological quantum field theory, knot theory, and the study of quantum computation and information.

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