Extension of the Poincar\'e Group and Non-Abelian Tensor Gauge Fields

In the recently proposed generalization of the Yang-Mills theory the group of gauge transformation gets essentially enlarged. This enlargement involves an elegant mixture of the internal and space-time symmetries. The resulting group is an extension of the Poincar\'e group with infinitely many generators which carry internal and space-time indices. This is similar to the super-symmetric extension of the Poincar\'e group, where instead of an anti-commuting spinor variable one should introduce a new vector variable. The construction of irreducible representations of the extended Poincar\'e algebra identifies a vector variable with the derivative of the Pauli-Lubanski vector over its length. As a result of this identification the generators of the gauge group have nonzero components only in the plane transversal to the momentum and are projecting out non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite space-like components.Comment: 21 page

Possible quantum kinematics. II. Non-minimal case

The quantum analogs of the N-dimensional Cayley-Klein spaces with different combinations of quantum and Cayley-Klein structures are described for non-minimal multipliers, which include the first and the second powers of contraction parameters in the transformation of deformation parameter. The noncommutative analogs of (N-1)-dimensional constant curvature spaces are introduced. Part of these spaces for N=5 are interpreted as the noncommutative analogs of (1+3) space-time models. As a result the wide variety of the quantum deformations of realistic kinematics are suggested.Comment: 13 pages, no figure

From Symmetry to Supersymmetry

This text is the draft of Julius Wess' contribution to the Proceedings of SUSY07 (KIT Karlsruhe) and to "Supersymmetry at the dawn of the LHC" in Eur. Phys. J. C59/2. The manuscript, which Wess could not finish before his death, has been edited for the publication.Comment: Feb.2009 - Contribution edited for the Proceedings SUSY07 (KIT Karlsruhe) and "Supersymmetry at the dawn of the LHC" in Eur. Phys. J. C59/

Spinning particle in an external linearized gravitational wave field

We study the interaction of a scalar and a spinning particle with a coherent linearized gravitational wave field treated as a classical spin two external field. The spin degrees of freedom of the spinning particle are described by skew-commuting variables. We derive the explicit expressions for the eigenfunctions and the Green's functions of the theory. The discussion is exact within the approximation of neglecting radiative corrections and we prove that the result is completely determined by the semiclassical contribution.Comment: 11 page

On contractions of classical basic superalgebras

We define a class of orthosymplectic $osp(m;j|2n;\omega)$ and unitary $sl(m;j|n;\epsilon)$ superalgebras which may be obtained from $osp(m|2n)$ and $sl(m|n)$ by contractions and analytic continuations in a similar way as the special linear, orthogonal and the symplectic Cayley-Klein algebras are obtained from the corresponding classical ones. Casimir operators of Cayley-Klein superalgebras are obtained from the corresponding operators of the basic superalgebras. Contractions of $sl(2|1)$ and $osp(3|2)$ are regarded as an examples.Comment: 15 pages, Late

Relation between confinement and higher symmetry restrictions for color particle motion

Quantum operators of coordinates and momentum components of a particle in the Minkowski spacetime can belong to the generalized Snyder-Yang algebra and produce a quantum phase space with three new constants in the general case. With account for the O(2,6) invariance in the quantum phase space of a color particle the equation of motion is obtained, which contains a oscillator rising potential. The presence of the oscillator potential can simulate a confinement of a color particle. A parameter of the oscillator potential is estimated and a relationship between current and constituent quark masses is obtained.Comment: 3 pages, style and typos corrected, more general case considered, main results unchange

Energy composition of the Universe: time-independent internal symmetry

The energy composition of the Universe, as emerged from the Type Ia supernova observations and the WMAP data, looks preposterously complex, -- but only at the first glance. In fact, its structure proves to be simple and regular. An analysis in terms of the Friedmann integral enables to recognize a remarkably simple time-independent covariant robust recipe of the cosmic mix: the numerical values of the Friedmann integral for vacuum, dark matter, baryons and radiation are approximately identical. The identity may be treated as a symmetry relation that unifies cosmic energies into a regular set, a quartet, with the Friedmann integral as its common genuine time-independent physical parameter. Such cosmic internal (non-geometrical) symmetry exists whenever cosmic energies themselves exist in nature. It is most natural for a finite Universe suggested by the WMAP data. A link to fundamental theory may be found under the assumption about a special significance of the electroweak energy scale in both particle physics and cosmology. A freeze-out model developed on this basis demonstrates that the physical nature of new symmetry might be due to the interplay between electroweak physics and gravity at the cosmic age of a few picoseconds. The big `hierarchy number' of particle physics represents the interplay in the model. This number quantifies the Friedmann integral and gives also a measure to some other basic cosmological figures and phenomena associated with new symmetry. In this way, cosmic internal symmetry provides a common ground for better understanding of old and recent problems that otherwise seem unrelated; the coincidence of the observed cosmic densities, the flatness of the co-moving space, the initial perturbations and their amplitude, the cosmic entropy are among them.Comment: 32 page

Cosmology and New Physics

A comparison of the standard models in particle physics and in cosmology demonstrates that they are not compatible, though both are well established. Basics of modern cosmology are briefly reviewed. It is argued that the measurements of the main cosmological parameters are achieved through many independent physical phenomena and this minimizes possible interpretation errors. It is shown that astronomy demands new physics beyond the frameworks of the (minimal) standard model in particle physics. More revolutionary modifications of the basic principles of the theory are also discussed.Comment: 37 pages, 5 figures; lectures presented at 9th International Moscow School of Physics (34th ITEP Winter School

A Pedagogical Review of Electroweak Symmetry Breaking Scenarios

We review different avenues of electroweak symmetry breaking explored over the years. This constitutes a timely exercise as the world's largest and the highest energy particle accelerator, namely, the Large Hadron Collider (LHC) at CERN near Geneva, has started running whose primary mission is to find the Higgs or some phenomena that mimic the effects of the Higgs, i.e. to unravel the mysteries of electroweak phase transition. In the beginning, we discuss the Standard Model Higgs mechanism. After that we review the Higgs sector of the Minimal Supersymmetric Standard Model. Then we take up three relatively recent ideas: Little Higgs, Gauge-Higgs Unification, and Higgsless scenarios. For the latter three cases, we first present the basic ideas and restrict our illustration to some instructive toy models to provide an intuitive feel of the underlying dynamics, and then discuss, for each of the three cases, how more realistic scenarios are constructed and how to decipher their experimental signatures. Wherever possible, we provide enough pedagogical details, which the beginners might find useful.Comment: 45 pages, Review based on a series of lectures; v2: 63 pages, substantially expanded, references added, to appear in `Reports on Progress in Physics

Search for Squarks and Gluinos in Events Containing Jets and a Large Imbalance in Transverse Energy

Using data corresponding to an integrated luminosity of 79 pb-1, D0 has searched for events containing multiple jets and large missing transverse energy in pbar-p collisions at sqrt(s)=1.8 TeV at the Fermilab Tevatron collider. Observing no significant excess beyond what is expected from the standard model, we set limits on the masses of squarks and gluinos and on the model parameters m_0 and m_1/2, in the framework of the minimal low-energy supergravity models of supersymmetry. For tan(beta) = 2 and A_0 = 0, with mu < 0, we exclude all models with m_squark < 250 GeV/c^2. For models with equal squark and gluino masses, we exclude m < 260 GeV/c^2.Comment: 10 pages, 3 figures, Submitted to PRL, Fixed typo on page bottom of p. 6 (QCD multijet background is 35.4 events