By van Nieuwenhuizen P.
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Additional resources for Advanced quantum gauge field theory
28 ↔ For example, for scalar QED there are derivative couplings eAµ ϕ∗ ∂ µ ϕ, and the propagator 0|T ∂µ ϕ(x)∂ν ϕ∗ (y)|0 of the Hamiltonian approach differs from the covariant expression ∂ ∂ ∗ which one uses in the Lagrangian approach by the noncovariant term ∂xµ ∂y ν 0|T ϕ(x)ϕ (y)|0 0 0 4 i¯ hδµ δν δ (x − y). (When a time derivative hits the theta function in the time-ordering symbol one obtains the equal-time commutator [ϕ(x), ∂ν ϕ∗ (y)] which is nonvanishing for ν = 0). One may distinguish between a covariant time-ordering T ∗ used in Lagrangian approaches and Lagrangian path integrals, and the T symbol of canonical approaches.
In England, Blackett and Occhialini decided to study cosmic rays, and as soon as they saw Anderson’s article they looked for positron events in their own plates, and found many, including several cases in which Einstein had already in 1925 come close to predicting antimatter . He had constructed a unified field theory for gravity and electromagnetism with the antisymmetric part of the metric equal to the Maxwell curvature, and had derived from P and T symmetry that a particle with the same mass but opposite charge to the electron should exist.
Dirac’s original approach in  did not need any subsidiary conditions on physical states. By using transverse vector potentials he had, in effect, solved the constraint divA = 0. 27 Dirac, Heisenberg and Pauli, Fermi and others, all used operator methods and canonical quantization, thus a Hamiltonian approach, to quantize QED, and they all The ghost and antighost fields are free fields in QED, and expanding them into modes, the annihilation operators vanish on states without c and p(b) quanta.