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Talk presented at the NATO Advanced Workshop on Electroweak Physics and the Early Universe: Sintra, Portugal, 1994. I summarize work done with Larry Yaffe on applying $\epsilon$ expansion techniques to the electroweak phase transition.
In these lectures I describe some of the open questions in the standard model relating to the nature and origin of mass, forces and matter and discuss some of the speculative theoretical ideas put forth in this regard. Some of the topics…
We discuss spacetime singularity resolution in the context of the gravity/gauge correspondence, for brane systems which give rise to gauge theories with eight supercharges and no hypermultiplets. The discussion is aimed at non-experts.…
A brief review of main features of the new approach named ``quantum geometrodynamics in extended phase space'' is given and its possible prospects are discussed. Gauge degrees of freedom are treated as a subsystem of the Universe which…
The changes of main paradigms on the structure and evolution of the Universe are reviewed. Two puzzles of the modern cosmology, the mean density of matter and the regularity of the Universe on large scales, as well as the possibility to…
In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is…
I give a general non-technical review of supersymmetry and its modern applications in phenomenology and quantum field theories at strong coupling. Invited Talk at the conference {\sl Frontiers of Fundamental Physics, FFP16, May 23-26, 2022,…
Numerous non-standard dynamics are described by contact-like effective interactions that can manifest themselves through deviations of the cross sections from the Standard Model predictions. If one such deviation were observed, one should…
The emphasis in the developmet of theories with more than three spatial dimensions has recently shifted towards ``brane world'' picture, which assumes that ordinary matter (with possible exceptions of gravitons and other, hypothetic,…
This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.
In this talk, I describe a few interesting physics beyond the standard model that are quite unique for $\gamma\gamma$ collisions, including large extra dimension model (ADD), warped extra dimension model (Randall-Sundrum) model, universal…
The new millennium's qualitative advances in relativistic heavy ion physics are in part due to, and are in part causing, a new appreciation for quantitative rigor in both experimental and theoretical work in the field. In these proceedings…
In our previous article Phys. Rev. Lett. 127 (2021) 271601, we announced a novel 'democratic' Lagrangian formulation of general nonlinear electrodynamics in four dimensions that features electric and magnetic potentials on equal footing.…
We live in a four dimensional world. But the idea of unification of fundamental interactions lead us to higher dimensional theories. Recently a new theory with extra dimensions has emerged, where only gravity propagates in the extra…
We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including…
The evolution of the extra dimension is investigated in the context of brane world cosmology. New cosmological solutions are found. In particular, solutions in the form of waves travelling along the extra dimension are identified.
Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…
An Effective Lagrangian description is useful for describing potential physics beyond the Standard Model. The method is illustrated by reference to interactions among the electroweak bosons ($W^\pm$ \& $Z^0$). The resulting estimates of the…
An elementary review of models and phenomenology for physics beyond the Standard Model (excluding supersymmetry). The emphasis is on LHC physics. Based upon a talk given at the Physics at LHC conference, Vienna, 13-17 July 2004.
These notes arose from a mini lecture series the author gave at the Early Career Researchers Workshop on Geometric Analysis and PDEs, held in January 2020 at the Matrix institute of the University of Melbourne. We discussed some classical…