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"We impose the Higgs mechanism to break the Grand Unified Theory based on SU(6) symmetry, SU(6) GUT. We investigate and search for the Higgs multiplets which are approriate to generate masses for both fermions and gauge bosons. We have found that the most minimal Higgs multiplets are < 15 >,< 20 > and < 21 > to realize three steps of symmetry breaking in SU(6) GUT down to the standar SU(2) × U(1) model. However within this minimal SU(6) GUT, we can reproduce only some fermions spectra as N4e, νe,N6e, Ne and d quarks, although we have deployed the most general forms of Higgs multiplets. On the other hand, the present approach have succeeded in generating the reguler gauge bosons, W±, Z0 and Aµ."

"The aim of the present monograph is to illuminate more subtle aspects featuring group theory for quantum mechanics, that is, the concept of dynamical symmetry. "

"Telah dibangun Lagrangian baru serta dilakukan perhitungan analitik tensor energi-momentum untuk fluida QCD yang mengandung suku viskositas. Suku viskositas ini dibuat dengan asumsi bahwa persamaan gerak yang diperoleh mereproduksi persamaan gerak hidrodinamika relativistik. Suku viskositas mengakibatkan perusakan simetri fluida QCD. Memakai Lagrangian yang telah dibangun, dihitung distribusi jumlah partikel memakai teori kinetik dan resolusi Cooper- Frye. Ditunjukkan bahwa distribusi jumlah partikel memiliki kontur yang samamdengan hasil perhitungan sebelumnya memakai persamaan gerak hidrodinamika relativistik.

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A new Lagrangian and energy momentum tensor for fluid QCD with viscous term have been developed and calculated analytically. The viscous term has been constructed assuming that the generated equation of motion should reproduce the known relativistic hydrodynamics. The viscous term induces symmetry breaking of fluid QCD. Using the Lagrangian, the particle number distribution has been calculated using kinetic theory and Cooper-Frye prescription. It is shown that the distribution has the same contour as previous results calculated using the equation of motion of relativistic hydrodynamics."

"Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures."

"This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure—the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key rôle in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence.The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrödinger operators."