QUANTIZATION OF RELATIVISTIC DIRAC FIELD AND THE SPIN STATISTICS THEOREM

Abstract

In this project, attempt was made to develop the basic ideas of second quantization for a relativistic Dirac field using Lagrangian formalism in the four-dimensional space. In particular, concentration was made on the quantization of the Dirac field, Lagrangian and Hamiltonian density, Energy-momentum Tensor, Spin Statistics Theorem, propagators for fermions. The project work showed how the relativistic Dirac field can be quantized to reveal on the spin of the electron using anti-commutation relations for creation and annihilation operators and proceeded to study the Spin Statistics Theorem, which states the particle with half-integer spin are fermions, whose field operators are quantized by anti-commutators. Particles with integer spin are bosons, and their field operators are quantized by commutators