  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.
