An Introduction to Quantum Field Theory

In conventional Dirac theory, the electron is treated as a structureless point particle in Minkowski space.

“In conventional Dirac theory [5,7,8], the electron is treated as a structureless point particle in Minkowski space.”

A Lorentz transformation acts entirely within Minkowski space, preserves the metric, maps four vectors to four vectors, and preserves intrinsic parity.

“A Lorentz transformation [5] acts entirely within Minkowski space.It preserves the metric, maps four vectors to four vectors, and preserves intrinsic parity.”

A photon mass term in the electromagnetic field equation can naturally arise from spontaneous symmetry breaking and the Higgs mechanism in quantum field theory, where photons acquire mass by eating massless Goldstone bosons.

“This type of electromagnetic field equations can naturally arise from spontaneous symmetry breaking and the Higgs mechanism in quantum field theory, where photons acquire a mass by eating massless Goldstone bosons.”

The model described by equations (25) and (26) is the curved spacetime version of the model in chapter 20.1 of Ref. [33].

“The model described by equations (25) and (26) is the curved spacetime version of the model in the chapter 20.1 of Ref. [33].”

An effective ξ A_a A^a term can naturally arise from spontaneous symmetry breaking by the Higgs mechanism if the electromagnetic field is coupled to a complex scalar field.

“Although ξ can just be a fundamental constant in nature, an effective ξA a term can naturally arise from spontaneous symmetry breaking by the Higgs mechanism if the electromagnetic field is coupled to a complex scalar field [33, 34].”

In the unitary gauge, φ_2 = 0, so the massless Goldstone bosons go away by a gauge transformation.

“Hence, in this unitary gauge [33, 34], we have φ 2 = 0. That is, the massless Goldstone bosons go away by a gauge transformation.”