4 papers
States of 2D Yang-Mills and Large-Volume Entanglement
Dmitry Melnikov, Jefferson T. Oliveira, Valmir Peixoto +1
We study entanglement in two-dimensional Yang-Mills theory, viewed as a quasi-topological model of emergent space. The most familiar class of states in this theory are states defin…
A Tutorial on Knots and Quantum Mechanics
Dmitry Melnikov
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In t…
Jones polynomials from matrix elements of tangles in a pseudounitary representation
Dmitry Melnikov
In these notes we review the calculation of Jones polynomials using a matrix representation of the braid group and Temperley-Lieb algebra. The pseudounitary representation that we…
Connectomes as Holographic States
Dmitry Melnikov
We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the para…