49 research outputs found
The Stueckelberg Field
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.Comment: 58 pages, revtex4 RMP format. Added references, minor improvements to
tex
Quantum -Poincare in Any Dimensions
The -deformation of the D-dimensional Poincar\'e algebra
with any signature is given. Further the quadratic Poisson brackets, determined
by the classical -matrix are calculated, and the quantum Poincar\'e group
"with noncommuting parameters" is obtained.Comment: (PLAIN TeX, 10 pp.
q-Deformation of Semisimple and Non-Semisimple Lie Algebras
We give an elementary introduction to the Drinfeld-Jimbo procedure of the quantum deformation Uq(g) of semisimple Lie algebras g. The q—Serre relations are discussed in some detail, in the Chevalley and the Cartan—Weyl basis. We review the real forms of g and Uq(g). The general procedure is illustrated by the examples Uq(sℓ(2)) and Uq (so(5, ℂ)). After some general considerations on non-semisimple Lie algebras, we discuss in detail the quantum deformation of the Poincaré algebra, involving the contraction of Uq(so(3, 2)). Some physical consequences are mentioned