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Solitons and boundaries
1. Solitons and Boundaries Delivered at CBPF Rio de Janeiro June 28, 2002 Gustav W Delius Department of Mathematics The University of York United Kingdom
17. Time advance during scattering The solitons experience a time advance while scattering through each other.
18. Breather solution A breather is formed from a soliton and an antisoliton oscillating around each other.
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22. Method of images Place an oppositely moving and inverted mirror particle behind the boundary Dirichlet boundary condition is automatically satisfied
30. Time advance during reflection For an attractive boundary condition the soliton experiences a time advance during reflection.
31. Time delay during reflection For a repulsive boundary condition the soliton experiences a time delay during reflection.
32. Boundary bound states A soliton can bind to its mirror antisoliton to form a boundary bound state, the boundary breather.
33. Integrable Boundary Conditions Saleur,Skorik,Warner, Nucl.Phys.B441(1995)421. Determines location of mirror solitons Determines location of third stationary soliton Ghoshal,Zamolodchikov, Int.Jour.Mod.Phys.A9(1994)3841.
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35. Quantum soliton states Classical solution: Quantum state: Vacuum Soliton Antisoliton Coleman, Classical lumps and their quantum descendants, in “New Phenomena in Subnuclear Physics”. Dashen, Hasslacher, Neveu, The particle spectrum in model field theories from semiclassical functional integral techniques , Phys.Rev.D11(1975)3424. Rapidity:
38. Soliton S-matrix Possible processes in sine-Gordon: Identical particles Transmission Reflection (does not happen classically)
39. Semi-classical limit Jackiw and Woo, Semiclassical scattering of quantized nonlinear waves, Phys.Rev.D12(1975)1643. Faddeev and Korepin, Quantum theory of solitons , Phys. Rep. 42 (1976) 1-87. Time delay Number of bound states Semiclassical phase shift
40. Factorization (Yang-Baxter eq.) Zamolodchikov and Zamolodchikov, Factorized S-Matrices in Two Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Theory Models , Ann. Phys. 120 (1979) 253 The exact S-matrix can be obtained by solving =