Symplectic Geometry and Quantization

Code	13321
Year	1
Semester	S1
ECTS Credits	10
Workload	OT(30H)/TP(30H)
Scientific area	Física e Matemática
Entry requirements	None
Learning outcomes	To address the issue of quantization of classical systems in a rigorous and integrated way.
Syllabus	1 . Symplectic spaces 2. Hamiltonian mechanics 3. Quantization in phase space 4. Introduction to geometric and deformation quantization 5. Introduction to path integral methods
Main Bibliography	R Berndt 2001 An Introduction to Symplectic Geometry, Am.Math.Soc. A Cannas da Silva 2008 Lectures on Symplectic Geometry, Springer C Esposito 2015 Formality Theory: From Poisson Structures to Deformation Quantization, Springer B Felsager 1998 Geometry, Particles, and Fields, Springer GB Folland 1989 Harmonic Analysis in Phase Space, Princeton Univ.Press J Glimm, A Jaffe 1987 Quantum Physics 2ed, Springer AA Kirillov 2001 Geometric Quantization, in Dynamical Systems IV: Symplectic Geometry and its Applications 2ed (eds. VI Arnol’d, SP Novikov), Springer NP Landsman 1998 Mathematical Topics between Classical and Quantum Mechanics, Springer JE Marsden, TS Ratiu 1999 Introduction to Mechanics and Symmetry 2ed, Springer JP Nunes 2014 Rev.Math.Phys. 26, 1430009 G Rudolph, M Schmidt 2013 Differential Geometry and Mathematical Physics I, Springer JM Souriau 1997 Structure of Dynamical Systems: A Symplectic View of Physics, Springer NMJ Woodhouse 1997 Geometric Quantization 2ed, Clarendon Pres
Language	Portuguese. Tutorial support is available in English.