Quantum Field Theory/Transformational properties of fields

Relativity principle and the group of coordinate transformations. The group of Lorentz transformations. Lie groups and Lie algebras. Lie algebra of the Rotation Group. Lie algebra of the Lorentz Group. Group Representations. Irreducible representations of the rotation group. Direct product of two irreducible representations. Reduction of the direct product into a direct sum -- Clebsch-Gordan theorem. Irreducible representations of the Lorentz group. Direct product of two irreducible representations. Parity transformation. Bilinear forms of bispinors. Dirac matrices.