Renormalization of the SU(2)-symmetric model of hadrodynamics

Abstract

It is proved that the SU(2)-symmetric model of hadrodynamics can well be set up on the gauge-invariance principle. The quantization of the model can readily be performed in the Lagrangian path-integral formalisms by using the Lagrangian undetermined multiplier method. Furthermore, it is shown that the quantum theory is invariant with respect to a kind of BRST-transformations. From the BRST-symmetry of the theory, the Ward-Takahashi identities satisfied by the generating functionals of full Green functions, connected Green functions and proper vertex functions are successively derived. As an application of the above Ward-Takahashi identities, the Ward-Takahashi identities obeyed by the propagators and various proper vertices are derived. Based on these identities, the propagators and vertices are perfectly renormalized. Especially, as a result of the renormalization, the Slavnov-Taylor identity satisfied by renormalization constants is natually deduced. To demonstrate the renormalizability of the theory, the one-loop renormalization of the theory is carried out by means of the mass-dependent momentum space subtraction and the renormalization group approach, giving an exact one-loop effective coupling constant and one-loop effective nucleon, pion and $ρ-$meson masses.