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Quantum Field Theory/Transformational properties of fields

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Relativity principle and the group of coordinate transformations. The group of Lorentz transformations.

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Lie groups and Lie algebras. Lie algebra of the Rotation Group. Lie algebra of the Lorentz Group.

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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.

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Irreducible representations of the Lorentz group. Direct product of two irreducible representations.

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Parity transformation. Bilinear forms of bispinors. Dirac matrices.

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