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The ad-hoc imposition of normal ordering on the Lagrangian, energy-momentumtensor and currents is a standard tool in quantum field theory (QFT) toeliminate infinite vacuum expectation values (v.e.v.) However, for fermionicexpressions these infinite terms are due to anti-particles only. This exposesan asymmetry in standard QFT, which can be traced back to a bias towardsparticles in the Dirac bra-ket notation. To counter this bias a new orderingprinciple (called the $\mathbb{R}$-product) is required which restores thesymmetry (or rather duality) between particles and anti-particles andeliminates the infinite v.e.v. While this $\mathbb{R}$-product was already usedin a bound-state application, this paper aims to give it a more generalfoundation and analyze its overall impact in QFT.  For boson fields the particle bias is hidden and the fields must first beexpanded into bilinear particle-anti-particle fermion operators. This newrepresentation also leads to vanishing v.e.v.'s and avoids some commontechnical problems in the quantization of vector fields, while it admits newconstant contributions that mimic the Higgs mechanism without unacceptablecontributions to the cosmological constant.  Since the $\mathbb{R}$-product does not apply between operators belonging todifferent 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 astandard bosonic form despite the fermionic representation. However, thefoundations of QFT are affected strongly as the new principle suggests that theStandard Model is an effective theory built (partly?) on massless bare quarks.

A new ordering principle in quantum field theory and its consequences