1995/12/21 by S. Penati, A. Refolli, D. Zanon · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Conserved quantity #Homogeneous space #Nonlinear Waves and Solitons #Quantization (signal processing) #Quantum #Quantum field theory #Toda lattice #hep-th
paper · pdf · doi:10.1016/0550-3213(96)00163-0
published as Nucl.Phys. B470 (1996) 396-418 · 26 pages, latex, no figures
arxiv created 1995/12/21 · openalex publication_date 1996/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we present a detailed study of the quantum conservation laws for Toda field theories defined on the half plane in the presence of a boundary perturbation. We show that total derivative terms added to the currents, while irrelevant at the classical level, become important at the quantum level and in general modify significantly the quantum boundary conservation. We consider the first nontrivial higher--spin currents for the simply laced a(1)n Toda theories: we find that the spin--three current leads to a quantum conserved charge only if the boundary potential is appropriately redefined through a finite renormalization. Contrary to the expectation we demonstrate instead that at spin four the classical symmetry does not survive quantization and we suspect that this feature will persist at higher--spin levels. Finally we examine the first nontrivial conservations at spin four for the d(2)3 and c(1)2 nonsimply laced Toda theories. In these cases the addition of total derivative terms to the bulk currents is necessary but sufficient to ensure the existence of corresponding quantum exact conserved charges.