A new ordering principle in quantum field theory and its consequences

Abstract

The ad-hoc imposition of normal ordering on the Lagrangian, energy-momentum tensor and currents is a standard tool in quantum field theory (QFT) to eliminate infinite vacuum expectation values (v.e.v.) However, for fermionic expressions these infinite terms are due to anti-particles only. This exposes an asymmetry in standard QFT, which can be traced back to a bias towards particles in the Dirac bra-ket notation. To counter this bias a new ordering principle (called the $\mathbb{R}$-product) is required which restores the symmetry (or rather duality) between particles and anti-particles and eliminates the infinite v.e.v. While this $\mathbb{R}$-product was already used in a bound-state application, this paper aims to give it a more general foundation and analyze its overall impact in QFT. For boson fields the particle bias is hidden and the fields must first be expanded into bilinear particle-anti-particle fermion operators. This new representation also leads to vanishing v.e.v.'s and avoids some common technical problems in the quantization of vector fields, while it admits new constant contributions that mimic the Higgs mechanism without unacceptable contributions to the cosmological constant. Since the $\mathbb{R}$-product does not apply between operators belonging to different space- time coordinates (e.g. propagators and vacuum condensates), most standard QFT calculations remain unaffected by this new principle, preserving those quantitative successes. The boson propagator also retains a standard bosonic form despite the fermionic representation. However, the foundations of QFT are affected strongly as the new principle suggests that the Standard Model is an effective theory built (partly?) on massless bare quarks.