Quantum Field Theory/Quantization of free fields

Spin 0 field Real and complex scalar fields. Klein-Gordon equation. Plane-wave (normal mode) solutions. Generation and anihilation operators. Hamiltonian. Commutation relations. Real and complex scalar fields. The equations of motion for a real scalar field can be obtained from the following lagrangian densities and the result is . The complex scalar field can be considered as a sum of two scalar fields: and , The Langrangian density of a complex scalar field is Klein-Gordon equation Klein-Gordon equation is precisely the equation of motion for the spin-0 particle as derived above: Spin 1/2 field Dirac equation The Dirac equation is given by: where is a four-dimensional Dirac spinor. The matrices obey the following anticommutation relation (known as the Dirac algebra): Notice that the Dirac algebra does not define a priori how many dimensions the matrices should be. For a four-dimensional Minkowski space, however, it turns out that the matrices have to be at least . Plane-wave (normal mode) solutions. Generation and annihilation operators. Hamiltonian. Anticommutation relations. Spin 1 field Massive spin 1 field. Additional (Lorentz) condition to eliminate spin-0. Massless spin 1 field. Gauge invariance. Quantization within Coulomb (radiation) gauge. Spin-statistics theorem. Discrete symmetries (C,P,T). CPT theorem.