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After Dirac introduced the monopole, topological objects have played increasingly important roles in physics. In this review we discuss the role of the knot, the most sophisticated topological object in physics, and related topological objects in various areas in physics. In particular, we discuss how the knots appear in Maxwells theory, Skyrme theory, and multi-component condensed matter physics.
Knotted solutions to electromagnetism are investigated as an independent subsector of the theory. We write down a Lagrangian and a Hamiltonian formulation of Batemans construction for the knotted electromagnetic solutions. We introduce a general defi
In the conventional formalism of physics, with 1-time, systems with different Hamiltonians or Lagrangians have different physical interpretations and are considered to be independent systems unrelated to each other. However, in this paper we construc
We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of spectral geometr
The recently conjectured knots-quivers correspondence relates gauge theoretic invariants of a knot $K$ in the 3-sphere to representation theory of a quiver $Q_{K}$ associated to the knot. In this paper we provide geometric and physical contexts for t
The Picard-Fuchs equation is a powerful mathematical tool which has numerous applications in physics, for it allows to evaluate integrals without resorting to direct integration techniques. We use this equation to calculate both the classical action