Quantum Field Theories

Initial success of quantum field theory was quantum electrodynamics (QED) that is still the paradigmatic example of a successful quantum field theory. Ordinarily, quantum mechanics (QM) cannot give an account of photons which constitute the prime case of relativistic 'particles'. At the speed c, a non-relativistic theory such as ordinary QM cannot give even an estimated description as photons have rest mass zero and similarly move in the vacuum. Photons are implicit in the emission and absorption processes which have to be postulated; for instance, when one of an atom's electrons makes a transition between energy levels. The formalism of QFT is required for an explicit explanation of photons. As soon as the conceptual framework of quantum mechanics was developed, a small group of theoreticians tried to extend quantum methods to electromagnetic fields. Modern developments of quantum field theory are as follows- Algebraic quantum field theory, Axiomatic quantum field theory, Topological quantum field theory (TQFT).

  • Conformal Field Theory
  • Non-abelian Gauge Theories
  • Scalar Fields
  • Dirac Equation
  • Quantum Electrodynamics
  • Renormalization

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