equations (namely, Gauss's law and Ampère's circuital law) using the substitutions: where i, j, k take the values 1, 2, and 3. Hamiltonian form The Hamiltonian density can be obtained with the usual relation, . Quantum electrodynamics and field theory The Lagrangian of quantum electrodynamics extends beyond the classical Lagrangian established in relativity to incorporate the creation and annihilation of photons (and electrons): where the first part in the right hand side, containing the Dirac spinor , represents the Dirac field. In quantum field theory it is used as the template for the gauge field strength tensor. By being employed in addition to the local interaction Lagrangian it reprises its usual role in QED. See also Classification of electromagnetic fields Covariant formulation of classical electromagnetism Electromagnetic stress–energy tensor Gluon field strength tensor Ricci calculus Riemann–Silberstein vector Notes References Electromagnetism Minkowski spacetime Theory of relativity Tensor physical quantities Tensors in general relativity