BCAM Course | Indefinite Inner Products and Non Self-Adjoint Operators

BCAM Course | Indefinite Inner Products and Non Self-Adjoint Operators 

This is a twelve-hour course that will take place over six lectures of 2 hours each, to be held twice weekly. March 4th - March 20th. Tuesday and Thursday from 14:30 to 16:30.

Pre-requisites: Linear Algebra. Functional analysis and Topology are recommended but not required.

References:

Math textbooks:

• T. Y. Azizov and I. S. Iokhvidov. "Linear operators in spaces with an indefinite metric." Trans. by E. R. Dawson.
• J. Bognar. "Indefnite Inner Product Spaces." https://doi.org/10.1007/978-3-642-65567-8
• I. Gohberg and M. G. Krein. "Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space."
• I. Gohberg, P. Lancaster, and L. Rodman. "Indefinite Linear Algebra and Applications." https://doi.org/10.1007/b137517
• T. Kato. "Perturbation theory for linear operators." https://doi.org/10.1007/978-3-642-66282-9
• J. R. Ringrose. "Compact non-self-adjoint operators."Physics textbooks:
• C.M. Bender et al. "PT Symmetry: In Quantum And Classical Physics." https://doi.org/10.1142/q0178
• N. Moiseyev. "Non-Hermitian Quantum Mechanics." https://doi.org/10.1017/cbo9780511976186

Physics review articles:

• Y. Ashida, Z. Gong, and M. Ueda. "Non-Hermitian physics". https://arxiv.org/abs/2006.01837
• C. M. Bender. "Making sense of non-Hermitian Hamiltonians". https://arxiv.org/abs/hep-th/0703096
• A. Mostafazadeh. "Pseudo-Hermitian representation of quantum mechanics". https://arxiv.org/abs/0810.5643