On the volume conjecture for classical spin networks
arXiv:0904.1734
Abstract
We prove an upper bound for the evaluation of all classical SU(2) spin networks conjectured by Garoufalidis and van der Veen. This implies one half of the analogue of the volume conjecture which they proposed for classical spin networks. We are also able to obtain the other half, namely, an exact determination of the spectral radius, for the special class of generalized drum graphs. Our proof uses a version of Feynman diagram calculus which we developed as a tool for the interpretation of the symbolic method of classical invariant theory, in a manner which is rigorous yet true to the spirit of the classical literature.
More than 200 diagrams, pdf is better for download. Minor corrections, references added
References in corpus (11)
- JaxoDraw: A graphical user interface for drawing Feynman diagrams
- Spin Foam Models for Quantum Gravity
- Asymptotics of Relativistic Spin Networks
- Non-perturbative summation over 3D discrete topologies
- Asymptotics of 10j symbols
- Spin network quantum simulator
- Asymptotics of the colored Jones function of a knot
- Feynman Diagrams in Algebraic Combinatorics
- Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
- The Higher Transvectants are Redundant
- On the Linear Combinants of a Binary Pencil