The Stueckelberg Field

By H. Ruegg, M. Ruiz-Altaba. 2003

368 citations recorded by the source corpus.

In 1938, Stueckelberg introduced a scalar field which makes an Abelian gauge theory massive but preserves gauge invariance. The Stueckelberg mechanism is the introduction of new fields to reveal a symmetry of a gauge--fixed theory. We first review the Stueckelberg mechanism in the massive Abelian gauge theory. We then extend this idea to the standard model, stueckelberging the hypercharge U(1) and thus giving a mass to the physical photon. This introduces an infrared regulator for the photon in the standard electroweak theory, along with a modification of the weak mixing angle accompanied by a plethora of new effects. Notably, neutrinos couple to the photon and charged leptons have also a pseudo-vector coupling. Finally, we review the historical influence of Stueckelberg's 1938 idea, which led to applications in many areas not anticipated by the author, such as strings. We describe the numerous proposals to generalize the Stueckelberg trick to the non-Abelian case with the aim to find alternatives to the standard model. Nevertheless, the Higgs mechanism in spontaneous symmetry breaking remains the only presently known way to give masses to non-Abelian vector fields in a renormalizable and unitary theory.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/707137e0b44f99c34f5e8214f8e187b38af91290

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Citations in the corpus

Hořava gravity at a Lifshitz point: A progress report (2017, methodology): “To restore the full general covariance, one way is to make the foliation dynamical by using the Stückelberg trick [194], in which the space-like hypersurfaces of t = constant in the (3+1) ADM decompositions are replaced by a scalar field φ = constant, which is always time-like [88, 195],”
Could dark energy be vector-like? (2004, methodology): “One of the arguments goes back to the Stueckelberg theory of massive vectors [39, 40].”
A Call for New Physics : The Muon Anomalous Magnetic Moment and Lepton Flavor Violation (2016, background): “spontaneous symmetry breaking governed by a new scalar field, or through the Stueckelberg mechanism [225, 226].”
Spin-half fermions with mass dimension one: theory, phenomenology, and dark matter (2004, background): “Since the known particles are described by quantum fields involving finite dimensional representation spaces of usual Wigner classes [6–8] — with certain questions about Higgs particles being deferred to another place [9, 10] — the dark matter may belong to the yet unexplored unusual Wigner classes.”
Λ scattering equations (2016, methodology): “A very familiar way of understanding this process is by analogy with the Stukelberg procedure for taking massless limits of massive vector bosons [56].”
Explaining dark matter and B decay anomalies with an Lμ − Lτ model (2016, methodology): “The mass of the Z ′ can be generated either through a Stueckelberg mechanism, thereby leaving the Lμ − Lτ symmetry unbroken [44, 45], or by a spontaneous symmetry breaking mechanism with the introduction of a scalar field, as described in Ref.”
The Dark Photon (2020, background): “This is also the case when the U(1) gauge bosons acquire a mass by means of the Stueckelberg Lagrangian (see (Ruegg and Ruiz-Altaba, 2004) for a review and the relevant references) LStu = − 1 2 M2aAaµA µ a − 1 2 M2bAbµA µ b −MaMbAaµA µ b .”