Related papers: Chern--Simons Terms as an Example of the Relations…
The essential role played by Chern--Simons terms in a variety of physical models provides yet another illustration of the unexpected but profound interactions between the two disciplines.
Some properties of Chern-Simons terms are presented and their physical utility is surveyed.
The physical content of Chern-Simons-action is discussed and it is shown that this action is proportional to the usual charged matter interaction term in electrodynamics.
The use of the physical variables in the fashion of Dirac in the three-dimensional Chern-Simons theories is presented. Our previous results are reinterpreted in a new aspect.
We consider models in which nonrelativistic matter fields interact with gauge fields whose dynamics are governed by the Chern-Simons term. The relevant equations of motion are derived and reduced dimensionally in time or in space.…
With two typical parent actions we have two kinds of dual worlds: i) one of which contains an electric as well as magnetic current, and ii) the other contains (generalized) Chern-Simons terms. All these fields are defined on a curved…
We study contact terms of conserved currents and the energy-momentum tensor in three-dimensional quantum field theory. They are associated with Chern-Simons terms for background fields. While the integer parts of these contact terms are…
It is well known that Chern-Simons Theories are in the constrained systems and their total Hamiltonians become identically zero, because of their gauge invariance. While treating the constraints quantum mechanially, it will be expected taht…
Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge field
The Chern--Simons term is used in the geometric theory of defects. The equilibrium equations with $\delta$-function source are explicitly solved with respect to the $SO(3)$ connection. This solution describes one straight linear…
An analog of Chern-Simons theory is developed in an algebro-geometric setting.
We describe some instances of the appearance of Chern's mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
Various applications of Chern-Simons theory in algebraic topology, in particular knot theory, condensed matter physics and cosmology are reviewed. Special attention is paid to appearances of Chern-Simons actions in the theory of the…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
Chern-Simons theory can be defined on a cell complex, such as a network of bubbles, which is not a (Hausdorff) manifold. Requiring gauge invariance determines the action, including interaction terms at the intersections, and imposes a…
We study dipole Chern-Simons theory with and without a cosmological constant in $2+1$ dimensions. We write the theory in a second order formulation and show that this leads to a fracton gauge theory coupled to Aristotelian geometry which…
The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think: they seem to play an important role in…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is…