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Renormalization in quantum field theory and the RiemannHilbert problem. II. The βfunction, diffeomorphisms and the renormalization group
 Comm. Math. Phys
"... We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given by evalu ..."
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Cited by 344 (39 self)
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We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given
A RIEMANNHILBERT PROBLEM IN A RIEMANN SURFACE ∗
"... Abstract One of the inspirations behind Peter Lax’s interest in dispersive integrable systems, as the small dispersion parameter goes to zero, comes from systems of ODEs discretizing 1dimensional compressible gas dynamics [17]. For example, an understanding of the asymptotic behavior of the Toda la ..."
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the method used was the method of Lax and Levermore [16], reducing the asymptotic problem to the solution of a minimization problem with constraints (an “equilibrium measure ” problem). Later, it was found that the asymptotic method of Deift and Zhou (analysis of the associated RiemannHilbert factorization
The Nsoliton of the focusing nonlinear Schrödinger equation for
 N large, Comm. Pure Appl. Math
"... Abstract. We present a detailed analysis of the solution of the focusing nonlinear Schrödinger equation with initial condition ψ(x, 0) = N sech(x) in the limit N → ∞. We begin by presenting new and more accurate numerical reconstructions of the Nsoliton by inverse scattering (numerical linear alge ..."
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Cited by 18 (1 self)
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Abstract. We present a detailed analysis of the solution of the focusing nonlinear Schrödinger equation with initial condition ψ(x, 0) = N sech(x) in the limit N → ∞. We begin by presenting new and more accurate numerical reconstructions of the Nsoliton by inverse scattering (numerical linear
ChernSimons Gauge Theory as a String Theory
, 2003
"... Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given spacetime interpretations. For instance, threedimensional ChernSimons gaug ..."
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Cited by 551 (14 self)
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Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given spacetime interpretations. For instance, threedimensional Chern
String theory and noncommutative geometry
 JHEP
, 1999
"... We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from ..."
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Cited by 801 (8 self)
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We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Results 1  10
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16,781