Renormalization of a distorted gauge-invariant theory

Abstract

We consider a new type of renormalizable theory involving massive Yang-Mills fields whose mass is generated by an intrinsic breakdown of the usual local gauge symmetry. However, the Lagrangian has a distorted gauge symmetry which leads to the Ward-Takahashi (WT) identities. Also, the theory is independent of the gauge parameter 5. We completely carry out an explicit renormalization at the one-loop level by exhibiting counterterms. defining the physical parameters, and computing all renormalization constants to check the WT identities. Our results indicate that the physical scalar can be removed from the physical spectrum and that perhaps the theory could become asymptotically free.

A confining quark model and new gauge symmetry

“…Since the generalized gauge transformations involve non-integrable phase factor (2) and the vector gauge functions, it appears necessary to modify Faddeev-Popov method [12] in order to the quantize taiji gauge fields and to remove unphysical amplitudes due to the interaction of the unphysical longitudinal and time-like components [13] of the massless confion. We assume that the Faddeev-Popov method can be suitably modified and applied to the more complicated taiji SU 3 symmetry involving the fourth-order gauge field equations.…”

“…It can be verified that the gauge condition (31) cannot be imposed for all times because the unphysical components of the taiji gauge field ∂ µ H µa do not satisfy the free equation, in contrast to that in quantum electrodynamics. The vacuum-to-vacuum amplitude of the model is [12,13]…”

The S-matrix and graviton self-energy in quantum Yang-Mills gravity

“…[9] Similar mechanism of cancellation occurs in any theory with gauge symmetry or distorted gauge symmetry, and in Yang-Mills gravity. [11,12,13] We follow Faddeev and Popov's approach to discuss how to fix a gauge for all times with the help of path integrals and derived the effective Lagrangian for quantum Yang-Mills gravity. [10,11] From the action (1) with the Lagrangian (2) and the gauge-fixing terms (3), we derived the Yang-Mills field equation…”

“…The delta function (12) is to maintain the gauge condition for all times. [12,14] The functional determinant detU in (12) is defined by [11,12]…”

“…The generating functional for connected Green's functions in gauge invariant gravity can be defined after the gauge condition is specified. [13] Similarly, in Yang-Mills gravity the generating functional for connected Green's functions (or the vacuum-to-vacuum amplitude) (19) can be written as [12] W…”