Applications of Self-Adjoint Extensions in Quantum Physics : Proceedings of a Conference Held at the Laboratory of Theoretical Physics, JINR Dubna, USSR, September 29 - October 1, 1987

The shared purpose in this collection of papers is to apply the theory of self-adjoint extensions of symmetry operators in various areas of physics. This allows the construction of exactly solvable models in quantum mechanics, quantum field theory, high energy physics, solid-state physics, microelectronics and other fields. The 20 papers selected for these proceedings give an overview of this field of research unparallelled in the published literature; in particular the views of the leading schools are clearly presented. The book will be an important source for researchers and graduate students in mathematical physics for many years to come. In these proceedings, researchers and graduate students in mathematical physics will find ways to construct exactly solvable models in quantum mechanics, quantum field theory, high energy physics, solid-state physics, microelectronics and other fields. Content: Front Matter....Pages - Zero-range interactions with an internal structure....Pages 3-11 Evolution equations and selfadjoint extensions....Pages 12-27 Energy-dependent interactions and the extension theory....Pages 28-39 On perturbations for self-adjoint generators of feller processes....Pages 40-54 Singular perturbations defined by forms....Pages 55-66 Covariant markovian random fields in four space-time dimensions with nonlinear electromagnetic interaction....Pages 69-83 Point interaction Hamiltonians for crystals with random defects....Pages 87-99 Scattering on a random point potential....Pages 100-114 Faddeev equations for three composite particles....Pages 117-137 On the point interaction of three particles....Pages 138-145 A resonating- group model with extended channel spaces....Pages 146-159 The problem of a few quasi-particles in solid-state physics....Pages 160-173 Surfaces with an internal structure....Pages 177-193 Spectral properties of the laplacian with attractive boundary conditions....Pages 194-202 Quantum junctions and the self-adjoint extensions theory....Pages 203-217 The extension theory and diffraction problems....Pages 218-229 Hamiltonians with additional kinetic energy terms on hypersurfaces....Pages 230-238 Thin lattices as waveguides....Pages 241-256 Quantum waveguides....Pages 257-266 An exactly solvable model of a crystal with non-point atoms....Pages 267-273 Back Matter....Pages -