Spectral Theory and Mathematical Physics

The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schr©œdinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

4.4. The Witten index of DA in the Special Case dim (H) < ∞

Preface; Lower Bounds for Sojourn Time in a Simple Shape Resonance Model; 1. Introduction; 2. Preliminaries and main result; 2.1. The model; 2.2. Energy-time uncertainty principle; 2.3. Main result; 3. Technicalities; 3.1. An ODE lemma; 3.2. Resolvent representation; 3.3. Proof of Theorem 2.1; References; Spectral Properties for Hamiltonians of Weak Interactions; 1. Introduction; 2. Interaction of the Gauge boson W± with an electron and a massless neutrino; 2.1. Rigorous definition of the model; 2.2. Limiting absorption principle and spectral properties

3. Interaction of the gauge boson Z0 with an electron and a positron 3.1. Rigorous definition of the model ; 3.1.1. The Fock spaces for electrons, positrons and Z0 bosons ; 3.1.2. The Hamiltonian.; 3.2. Limiting absorbtion principle and spectral properties; 4. Prospectives; Acknowledgement.; References; Magnetic Laplacian in Sharp Three-dimensional Cones; 1. Introduction; 1.1. Motivation; 1.2. Main results; 1.2.1. Upper bound for the first Rayleigh quotients.; 1.2.2. Convergence of the bottom of essential spectrum.; 1.2.3. Corner concentration in the semiclassical framework.

1.2.4. Outline of the paper. 2. Upper bound for the fir…