Induced Representations of the Two Parametric Quantum Deformation Upq_{pq}[gl(2/2)]

The two-parametric quantum superalgebra $U_{p,q}[gl(2/2)]$ and its induced representations are considered. A method for constructing all finite-dimensional irreducible representations of this quantum superalgebra is also described in detail. It turns out that finite-dimensional representations of the two-parametric $U_{p,q}[gl(2/2)]$, even at generic deformation parameters, are not simply trivial deformations from those of the classical superalgebra $gl(2/2)$, unlike the one-parametric cases.Comment: Latex, 40 pages, no figure. To appear in J. Math. Phys. 41 (2000

Was the Higgs boson discovered?

The standard model has postulated the existence of a scalar boson, named the Higgs boson. This boson plays a central role in a symmetry breaking scheme called the Brout-Englert-Higgs mechanism (or the Brout-Englert-Higgs-Guralnik-Hagen-Kibble mechanism, for completeness) making the standard model realistic. However, until recently at least, the 50-year-long-sought Higgs boson had remained the only particle in the standard model not yet discovered experimentally. It is the last but very important missing ingredient of the standard model. Therefore, searching for the Higgs boson is a crucial task and an important mission of particle physics. For this purpose, many theoretical works have been done and different experiments have been organized. It may be said in particular that to search for the Higgs boson has been one of the ultimate goals of building and running the LHC, the world's largest and most powerful particle accelerator, at CERN, which is a great combination of science and technology. Recently, in the summer of 2012, ATLAS and CMS, the two biggest and general-purpose LHC collaborations, announced the discovery of a new boson with a mass around 125 GeV. Since then, for over two years, ATLAS, CMS and other collaborations have carried out intensive investigations on the newly discovered boson to confirm that this new boson is really the Higgs boson (of the standard model). It is a triumph of science and technology and international cooperation. Here, we will review the main results of these investigations following a brief introduction to the Higgs boson within the theoretical framework of the standard model and Brout-Englert-Higgs mechanism as well as a theoretical and experimental background of its search. This paper may attract interest of not only particle physicists but also a broader audience.Comment: LateX, 23 pages, 01 table, 9 figures. To appear in Commun. Phys. Version 2: Minor changes, two references adde

Finite-Dimensional Representations of the Quantum Superalgebra Uq_{q}[gl(2/2)]: I. Typical representations at generic qq

In the present paper we construct all typical finite-dimensional representations of the quantum Lie superalgebra $U_{q}[gl(2/2)]$ at generic deformation parameter $q$. As in the non-deformed case the finite-dimensional $U_{q}[gl(2/2)]$-module $W^{q}$ obtained is irreducible and can be decomposed into finite-dimensional irreducible $U_{q}[gl(2)\oplus gl(2)]$-submodules $V^{q}_{k}$Comment: published version. Some formulae are rewritten in more compact for

Irreducible representations of Upq[gl(2/2)]

The two-parametric quantum superalgebra $U_{pq}[gl(2/2)]$ and its representations are considered. All finite-dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and nontypical ones according to a proposition proved in the present paper. This proposition is a nontrivial deformation from the one for the classical superalgebra gl(2/2), unlike the case of one-parametric deformations.Comment: Latex, 8 pages. A reference added in v.