Lie Groups in Physics
by G. 't Hooft, M. J. G. Veltman
Publisher: Utrecht University 2007
Number of pages: 75
Contents: Quantum mechanics and rotation invariance; The group of rotations in three dimensions; More about representations; Ladder operators; The group SU(2); Spin and angular distributions; Isospin; The Hydrogen Atom; The group SU(3); Representations of SU(N).
Download or read it online for free here:
by Boris Dubrovin - SISSA
These are lecture notes on various topics in analytic theory of differential equations: Singular points of solutions to analytic differential equations; Monodromy of linear differential operators with rational coefficients.
by G.Sardanashvily - arXiv
We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. This is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and systems with time-dependent parameters.
by J.F. Carinena, J. de Lucas - arXiv
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping.
by Eric L. Michelsen - UCSD
This text covers some of the unusual or challenging concepts in graduate mathematical physics. This work is meant to be used with any standard text, to help emphasize those things that are most confusing for new students.