Massive abelian gauge fields are renormalizable while massive non-abelian gauge fields are not.
the verdict
CONTESTED
contested - evenly split
refutedsupported
the weight of evidence
3 sources for · 3 against
The literature presents mixed evidence, indicating that while some non-abelian gauge field formulations can achieve power-counting renormalizability under specific extensions, others require special symmetries or are studied as dynamical models.
The Abelian Embedding Formulation of the Stueckelberg Model and its Power-counting Renormalizable Extension
We elucidate the geometry of the polynomial formulation of the non-abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent BRST differential exists allowing to implement the constraint on the sigma field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-abelian gauge fields. As all versions of the Stueckelberg theory, also the abelian embedding formulation yields a non power-counting renormalizable theory in D=4. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the abelian embedding formalism.
Published as: Phys.Rev.D73:065024,2006
DOI: 10.1103/PhysRevD.73.065024
arXiv categories: hep-th
We study non-Abelian fields in the context of very special relativity (VSR). For this, we define the covariant derivative and the gauge field gauge transformations, both of them involving a fixed null vector nμ, related to the VSR breaking of the Lorentz group to the Hom(2) or Sim(2) subgroups. As in the Abelian case, the gauge field becomes massive. Moreover, we show that the VSR gauge transformations form a closed algebra. We then write actions coupling the gauge field to various matter fields (bosonic and fermionic). We mention how we can use the spontaneous symmetry-breaking mechanism to give a flavor-dependent VSR mass to the gauge bosons. Finally, we quantize the model using the Becchi-Rouet-Stora-Tyutin formalism to fix the gauge. The model is renormalizable and unitary and for non-Abelian groups, asymptotically free.
We elucidate the geometry of the polynomial formulation of the non-abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent BRST differential exists allowing to implement the constraint on the sigma field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-abelian gauge fields. As all versions of the Stueckelberg theory, also the abelian embedding formulation yields a non power-counting renormalizable theory in D=4. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the abelian embedding formalism.
monopoles are not allowed. For non-Abelian gauge theory, there is no affine limit, and the Higgs oscillations cannot be too much more massive than the
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other being fermions) would be considered massless, but measurements show that the W+, W−, and Z0 bosons actually have relatively large masses of around 80 GeV/c2 (i
To have arbitrarily small charges requires that the U(1) is not the circle of unit complex numbers under multiplication, but the real numbers under addition, which is only different in the global topology. Such a U(1) group is non-compact. The field θ transforms as an affine representation of the gauge group. Among the allowed gauge groups, only non-compact U(1) admits affine representations, and the U(1) of electromagnetism is experimentally known to be compact, since charge quantization holds to extremely high accuracy.
The Higgs condensate in this model has infinitesimal charge, so interactions with the Higgs boson do not violate charge conservation. The theory of quantum electrodynamics with a massive photon is still a renormalizable theory, one in which electric charge is still conserved, but magnetic monopoles are not allowed. For non-Abelian gauge theory, there is no affine limit, and the Higgs oscillations cannot be too much more massive than the vectors.
A proof of renormalizability of the theory of the dynamical non-Abelian two-form is given using the Zinn-Justin equation. Two previously unknown symmetries of the quantum action, different from the BRST symmetry, are needed for the proof. One of these is a gauge fermion dependent nilpotent symmetry, while the other mixes different fields with the same transformation properties. The BRST symmetry itself is extended to include a shift transformation by use of an anticommuting constant. These three symmetries restrict the form of the quantum action up to arbitrary order in perturbation theory. The results show that it is possible to have a renormalizable theory of massive vector bosons in four dimensions without a residual Higgs boson.
We examine a model for massive vector mesons in four dimensions proposed by Freedman and Townsend, where the masses for non-Abelian vector gauge fields are generated without symmetry breaking through a gauge invariant coupling to anti-symmetric tensor fields. The model is quantized using the formalism of Batalin and Vilkovisky. While the Abelian version immediately gives a renormalizable model for massive vector fields, it is shown that in the non-Abelian case the addition of an extra gauge invariant term in the initial Lagrangian leads to an ultraviolet behavior consistent with power-counting renormalizability.
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