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This article is an interdisciplinary review and an on-going progress report over the last few years made by myself and collaborators in certain fundamental subjects on two major theoretic branches in mathematics and theoretical physics:…
A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…
Contents * Introduction -- Why $S^1$-extended phase space? -- Why central extensions of classical symmetries? * Central extension \Gt of a group $G$ -- Group cohomology -- Cohomology and contractions: Pseudo-cohomology -- Principal bundle…
Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations…
This textbook introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…
This paper will consist of a selected, personal view of some of the issues associated with the intersections of nuclear and particle physics. As well as touching on the recent developments we will attempt to look at how those aspects of the…
Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later…
This paper studies the compatibility of having a grand unification scheme for particle physics, while at the same time having a perturbative string theory description of such a scheme on a D-brane. This is studied in a model independent…
Modern cosmology has created a tight link between particle physics / field theory and a wealth of new observational data on the structure of the Universe. These lecture notes focus on some of the most important aspects concerning the…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
The ability to categorize problems based upon underlying principles, rather than contexts, is considered a hallmark of expertise in physics problem solving. With inspiration from a classic study by Chi, Feltovich, and Glaser, we compared…
The advent of high-resolution electron and scanning probe microscopy imaging has opened the floodgates for acquiring atomically resolved images of bulk materials, 2D materials, and surfaces. This plethora of data contains an immense volume…
The physics of supersymmetry is reviewed from the perspective of physics at ever increasing energies. Starting from the minimal supersymmetric extension of the Standard Model at the electroweak scale, we proceed to higher energies seeking…
Grand Unification of all forces has been a well motivated paradigm for particle physics. This subject has been recently revisited in the context of string theory, leading to a geometric reformulation of the idea of unification of forces.…
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
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…
A string-theoretic structure of the standard model is defined having a 4-D quantum gravity metric consistent with topological and algebraic first principles. Unique topological diagrams of string states, strong and weak interactions and…
A new pseudoclassical supersymmetrical model of a spinning particle in 2+1 dimensions is proposed. Different ways of its quantization are discussed. They all reproduce the minimal quantum theory of the particle.
The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among matter with different levels of hierarchy is appreciated. It is shown that the generic perturbation…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…