Network Models: Action formulation
arXiv:0904.2688 · doi:10.1016/j.nuclphysb.2009.09.033
Abstract
We develop a technique to formulate quantum field theory on arbitrary network, based on different, randomly disposed sets of scattering's. We define R-matrix of the whole network as a product of R-matrices attached to each of scattering nods. Then an action for a network in terms of fermionic fields is formulated, which allows to calculate the transition amplitudes as their Green functions. On so-called bubble and triangle diagrams it is shown that the method produces the same results as the one which uses the generalized star product. The approach allows to extend network models by including multiparticle interactions at the scattering nods.
27 pages, 9 figures
References in corpus (19)
- Kirchhoff's Rule for Quantum Wires
- Junctions of three quantum wires
- The Generalized Star Product and the Factorization of Scattering Matrices on Graphs
- Bosonization and Scale Invariance on Quantum Wires
- Quantum Fields on Star Graphs
- Reflection-Transmission Algebras
- Junctions of one-dimensional quantum wires - correlation effects in transport
- Inter-edge interactions and novel fixed points at a junction of quantum Hall line junctions
- The inverse scattering problem for metric graphs and the traveling salesman problem
- Fermionic R-Operator and Integrability of the One-Dimensional Hubbard Model
- Integrable Chain Model with Additional Staggered Model Parameter
- Edge Excitations of an Incompressible Fermionic Liquid in a Disorder Magnetic Field
- Fermionisation of the Spin-S Uimin-Lai-Sutherland Model: Generalisation of Supersymmetric t-J Model to Spin-S
- Finite Temperature Quantum Field Theory with Impurities
- On the theory of plateau-plateau transitions in Quantum Hall Effect
- Algebraic approach to multiple defects on the line and application to Casimir force
- Bosonization and Vertex Algebras with Defects
- Grassmann-Gaussian integrals and generalized star products
- An Integrable Model with non-reducible three particle R-Matrix
Cited by in corpus (10)
- Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
- Non-equilibrium Steady States of Quantum Systems on Star Graphs
- Quantum wire junctions breaking time reversal invariance
- Quantum Fields on Star Graphs with Bound States at the Vertex
- Finite propagation speed and causal free quantum fields on networks
- Direct computation of scattering matrices for general quantum graphs
- Off-critical Luttinger Junctions
- Quantum Wire Network with Magnetic Flux
- A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces
- Integrable Defects at Junctions within a Network