Mathematical Methods for Physics

Esko Keski-Vakkuri received his Ph.D. in physics from Massachusetts Institute of Technology in 1995, and is currently a senior faculty member at the University of Helsinki. He has previously held positions at the California Institute of Technology and Uppsala University. His research is focused on string theory, black holes, holographic duality, and quantum information. Claus K. Montonen received his Ph.D. from the University of Cambridge in 1974 and later held positions at the Université de Paris XI (CNRS), the Research Institute for Theoretical Physics, Helsinki, and CERN. He held various senior faculty positions in the Department of Physics at the University of Helsinki from 1978 until his retirement in 2011, where he was responsible for curriculum design in theoretical physics. His research interests are in S-matrix theory, string theory and quantum field theory, having made major contributions to early string theory and duality in field and string theory. Marco Panero received his Ph.D. in physics from the University of Turin in 2003, after which he held postdoctoral positions at the Dublin Institute for Advanced Studies, the University of Regensburg, ETH Zurich, the University of Helsinki, and the Autonomous University of Madrid. Since 2014 he has been an Associate Professor in physics at the University of Turin. His main research interests are in lattice field theory and in theoretical high-energy physics.

1. Introduction; 2. Group theory; 3. Representation theory of groups; 4. Differentiable manifolds; 5. Riemannian geometry; 6. Semisimple Lie algebras and their unitary representations; Appendix A; References; Index.