Central Results in Hermite Forms

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Decomposition of Group Algebras

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Lie Algebra: Vector Space and Multiplication Law

Covers Lie Algebra, focusing on vector space and multiplication law.

Lie Groups and Lorentz Transformations

Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.

McKay Correspondence and Coxeter Groups

Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.

Weil Representation and Heis Operators

Covers the Weil representation, Heis operators, Stone-Neumann theorem, unitary operators, Lie algebra structure, and symplectic form.

Lie Algebra Representation

Delves into Lie algebra representation and Lorentz subgroup concepts.

Quantum Field Theory: Poincaré Group

Explores Einsteinian relativity, the Lorentz group, and Poincaré transformations, emphasizing proper and non-orthochronous components.

Symmetry and Group Theory: Exercise Set 4

Explores symmetry operations, isomorphic representations, and three-dimensional group representations.

QED: Gauge Theories

Covers Quantum Electrodynamics (QED), instantons, Feynman rules, and gauge theories in modern particle physics.

Quantum Field Theory: Exo Session 4

Covers exercises on Schur's lemma and the Jacobi identity in Quantum Field Theory.