Path integral quantization of generalized quantum electrodynamics

In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac’s methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green’s functions and a discussion about the obtained results are presented.

Figure 1

The SDFE for the photon propagator.

Figure 2

The SDFE for the electron propagator.

Figure 3

The SDFE for the vertex function.

Figure 4

Electron self-energy diagram.

Figure 5

Vertex part diagram.