Related papers: Physico--Mathematical Interactions: The Chern--Sim…
We introduce Chern-Simons interaction into the three dimensional four-fermi theory, ad suggest a possible line of non-Gaussian infrared stable fixed points of the four-fermi operator, this line is characterized by the Chern-Simons coupling.
One source of beauty in mathematics is totally unexpected connections between two fundamentally different objects. For instance, is it not surprising that the time period of a real simple pendulum is linked with a function arising out of…
It is suggested that the original, minimal Kaluza-Klein theory should be extended by adding a 5-dimensional version of the Gibbons-Hawking gravitational surface term. It is then demonstrated that the usual dimensional reduction of the newly…
Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex…
Researchers in physics education have advocated both for including modeling in science classrooms as well as promoting student engagement with sensemaking. These two processes facilitate the generation of new knowledge by connecting to…
Although we accept that Physics is, as a last resort, an experimental science, the relationship between theory and experiment is far away from being trivial. Any experiment is always explained within a determinate theoretical context and,…
Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…
On the basis of Chern-Simons field-theoretical description we propose a simple method for derivation of model interactions for Pfaffian paired states. We verify the method in the case of Pfaffian (i.e. Moore - Read) state, and derive a…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
We consider the asymptoic behaviour of the Chern - Simons (CS) theory with matter in curved space - time. The asymptotics of effective couplings are discussed.
We consider quantum field theories on supermanifolds using integral forms. The latter are used to define a geometric theory of integration and they are essential for a consistent action principle. The construction relies on Picture Changing…
We review recent efforts to machine learn relations between knot invariants. Because these knot invariants have meaning in physics, we explore aspects of Chern-Simons theory and higher dimensional gauge theories. The goal of this work is to…
We propose a new, generic mechanism of inflation mediated by a balance between potential forces and a Chern-Simons interaction. Such quasi-topological interactions are ubiquitous in string theory. In the minisuperspace approximation, their…
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and give rise to a variety of…
Scientific communication inside and outside the classroom is the main means for providing an adequate understanding of how science and technological innovation relate to society. In order to achieve this goal, it is important to explore new…
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…
In the present article, Chern-Simons gauge theory and its relationship with gravity are revisited from a geometrical viewpoint. In this setting, our goals are twofold: In one hand, to show how to represent the family of variational problems…
When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (covary).…
With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many…
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.