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The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
Implications of the recent results on neutrino masses and mixing to underlying new physics are considered. Various approaches to physics behind neutrino mass are described which include the tri-bimaximal mixing and flavor symmetries, the…
The topics discussed in this lecture include: general properties of neutrinos in the SM, the theory of neutrino masses and mixings (Dirac and Majorana), neutrino oscillations both in vacuum and in matter, an overview of the experimental…
After discussing alternative scenarios for the origins of the electroweak symmetry breaking, I briefly review the experimental status of the Standard Model. I explore further both the hints for, and constraints on, supposing that that a…
In these lecture notes, an introduction to superstring theory is presented. Classical strings, covariant and light-cone quantization, supersymmetric strings, anomaly cancelation, compactification, T-duality, supersymmetry breaking, and…
This talk, dedicated to the memory of G. Giacomelli, introduced the round table on neutrinos held in February 2014. The topics selected for the discussion are: 1) the neutrinoless double beta decay rate (interpretation in terms of light…
Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are…
Signals for new, non-supersymmetric physics at hadron colliders are reviewed. We focus on extended gauge sectors and new matter particles. {Presented at the {\it 10th Topical Workshop on Proton-Antiproton Collider Physics}, Batavia, IL,…
This is a colloquium style pedagogical introduction to the paradigm of large extra dimensions. To be published in the Proceedings of the Workshop "Crossing the boundaries: Gauge dynamics at strong coupling," (May 14 - 17, 2009,…
This paper follows recent steps towards a nonassociative quantum theory and points out the mathematical structure behind the proposed modifications to conventional quantum theory. An N=1 supersymmetry model and a strong force glueball…
The biggest question in beyond the standard model physics is what are the scales of new physics. Ideas about scales, as well as experimental evidence and constraints, are surveyed for a variety of possible forms of new physics:…
A review of supersymmetry theory and phenomenology is presented. Topics discussed include: gravity-mediated (SUGRA) and gauge-mediated (GMSB) supersymmetry breaking models; an overview of non-universal soft-supersymmetry-breaking masses and…
Supergravities in four and higher dimensions are reviewed. We discuss the action and its local symmetries of N=1 supergravity in four dimensions, possible types of spinors in various dimensions, field contents of supergravity multiplets,…
We construct a new extension of the Poincar\'e superalgebra in eleven dimensions which contains super one-, two- and five-form charges. The latter two are associated with the supermembrane and the superfivebrane of M-theory. Using the…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric,…
Nonreciprocal theories are used to model a broad array of non-equilibrium phenomena found in nature ranging from biological systems like networks of neurons to the behavior of overflowing water fountains. This includes systems broadly…
Quarks and leptons charges and interactions are derived from gauge theories associated with symmetries. Their space-time labels come from representations of the non-compact algebra of Special Relativity. Common to these descriptions are the…
These notes are a summary of lectures given at the Instituto de Astronomia of the Universidad Nacional Autonoma de Mexico (UNAM), the Dipartimento di Fisica of the Universita degli studi di Salerno (Italy), and the Instituto de Fisica…
I discuss gauge and global symmetries in particle physics, condensed matter physics, and quantum gravity. In a modern understanding, global symmetries are approximate and gauge symmetries may be emergent. (Based on a lecture at the April,…