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Lecture
Nilpotent Lie Groups
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General Fields: Lorentz Representations
Covers the representation of Lorentz transformations through general fields and the consequences of symmetry.
Weil Representation and Heis Operators
Covers the Weil representation, Heis operators, Stone-Neumann theorem, unitary operators, Lie algebra structure, and symplectic form.
Lie Groups and Lorentz Transformations
Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.
Exponential Maps: Properties and Applications in Lie Groups
Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.
Quantum Field Theory: Poincaré Group
Explores Einsteinian relativity, the Lorentz group, and Poincaré transformations, emphasizing proper and non-orthochronous components.
Symmetry: Noether Theorem
Explores the consequences of symmetry, focusing on the Noether Theorem and coordinated charges in Lie groups.
Symplectic Geometry
Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.
Lie Algebras: Introduction and Structure
Introduces Lie algebras, vector spaces with a special bracket operation.
Lie Groups: SU(2) and SO(3)
Covers Lie groups, focusing on SU(2) and SO(3), discussing group structure and representations.
Lie Group: Structure and Transformations
Explores Lie groups, their structure, and applications in transformations.
