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Quantum Field Theory on Star Graphs
High Energy Physics - Theory · Submitted 18 Jan 2008
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim These results are applied for deriving the charge and spin transport, which have interesting physical features.
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The abstract, sentence by sentence
We discuss some basic aspects of quantum fields on star graphs, focusing on boundary conditions, symmetries and scale invariance in particular. We investigate the four-fermion bulk interaction in detail. Using bosonization and vertex operators, we solve the model exactly for scale invariant boundary conditions, formulated in terms of the fermion current and without dissipation. The critical points are classified and determined explicitly. These results are applied for deriving the charge and spin transport, which have interesting physical features.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss some basic aspects of quantum fields on star graphs, focusing on boundary conditions, symmetries and scale invariance in particular. | contribution 0.61 | 0.78 | 0.05 | asserted 0.75 |
| s1 | We investigate the four-fermion bulk interaction in detail. | contribution 1.00 | 0.93 | 0.04 | asserted 0.92 |
| s2 | Using bosonization and vertex operators, we solve the model exactly for scale invariant boundary conditions, formulated in terms of the fermion current and without dissipation. | method 0.72 | 0.96 | 0.28 | asserted 1.00 |
| s3 | The critical points are classified and determined explicitly. | result 0.92 | 0.92 | 0.14 | asserted 1.00 |
| s4 | These results are applied for deriving the charge and spin transport, which have interesting physical features. | result 0.66 | 0.94 | 0.32 | asserted 1.00 |
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The paper
Original abstract
We discuss some basic aspects of quantum fields on star graphs, focusing on boundary conditions, symmetries and scale invariance in particular. We investigate the four-fermion bulk interaction in detail. Using bosonization and vertex operators, we solve the model exactly for scale invariant boundary conditions, formulated in terms of the fermion current and without dissipation. The critical points are classified and determined explicitly. These results are applied for deriving the charge and spin transport, which have interesting physical features.
Human review
References
How the literature uses it
21 arXiv papers cite this in 48 sentences
Papers citing it · 30 sentences without a confident label
Builds on it 1 paper
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We will show now that this strategy, which works [ref] nicely at criticality, can be extended to off-critical boundary conditions as well.
Off-critical Luttinger Junctions · Bulk theory and boundary conditions · 0.93
Compares with it 2 papers
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In the appendix A of Ref. [ref] the conductance is written in terms of an $n×n$ $R$, which agrees with the results here and elsewhere [ref] .
Junctions of anyonic Luttinger wires · Boundary conditions and symmetries · 0.95
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Non-linear effects are absent in the critical regime under consideration, which implies the conductance tensor [equation] We see that the NESS approach, adopted in this paper, confirms the result for $$, obtained previously for $=̨1$ by different methods, including renormalization group techniques [ref] , linear response theory [ref] and conformal field theory [ref] .
Luttinger Liquid in Non-equilibrium Steady State · Charge and heat transport · 0.98
Cites it as background 12 papers
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In order not to overload the text with heavy expressions, we will only present hereafter the result for scale invariant R-matrices as defined in [ref] , [ref] , [ref] .
Network Models: Action formulation · Bubble Diagram · 0.81
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In the last few years there has been a boom in the study of transport properties at the junction of multiple quantum wires [ref] .
Junctions of anyonic Luttinger wires · Introduction · 0.98
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More recently, the low energy dynamics of multiple ≪wires connected to a junction have also been studied in detail [ref] and several interesting fixed points have been found, including continuous one-parameter families of fixed points [ref] .
A systematic stability analysis of the renormalisation group flow for the normal-superconductor-normal junction of Luttinger liquid wires · Introduction · 0.87
What it cites · 22 sentences without a confident label
Builds on 1 paper
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It is quite natural therefore to extend [ref] the bosonization procedure on the line to star graphs.
Bosonization and Scale Invariance on Quantum Wires · Bosonization and vertex operators · 1.00
Uses the method or tool of 5 papers
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Our construction is based on the point-like character of the boundary interactions at the vertex, the theory of self-adjoint extension of Hermitian operators on graphs [ref] - [ref] and the algebraic technique [ref] , [ref] , [ref] - [ref] for dealing with defects in QFT.
Algebraic approach to multiple defects on the line and application to Casimir force · Outlook and perspectives · 0.97
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Our construction is based on the point-like character of the boundary interactions at the vertex, the theory of self-adjoint extension of Hermitian operators on graphs [ref] - [ref] and the algebraic technique [ref] , [ref] , [ref] - [ref] for dealing with defects in QFT.
Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line · Outlook and perspectives · 0.97
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Our construction is based on the point-like character of the boundary interactions at the vertex, the theory of self-adjoint extension of Hermitian operators on graphs [ref] - [ref] and the algebraic technique [ref] , [ref] , [ref] - [ref] for dealing with defects in QFT.
Boundary Exchange Algebras and Scattering on the Half Line · Outlook and perspectives · 0.97
Cites as background 2 papers
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Referring for the details concerning $ℱ(A)$ and $𝒢_β(A)$ to [ref] and [ref] , we collect below only the two-point expectation values of ${a_i(k), a^*_i(k) : k∈}$.
Finite Temperature Quantum Field Theory with Impurities · Representations of the RT algebra $𝒜$ · 0.80
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Referring for the details concerning $ℱ(A)$ and $𝒢_β(A)$ to [ref] and [ref] , we collect below only the two-point expectation values of ${a_i(k), a^*_i(k) : k∈}$.
Boundary Exchange Algebras and Scattering on the Half Line · Representations of the RT algebra $𝒜$ · 0.80
Discussion
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