Topological Quantum Field Theory
In TQFT, the focus is on topological invariants such as the Jones polynomial, which describe the topology of a knot or a link in three-dimensional space. These invariants are computed using a topological field theory, which is a quantum field theory that is invariant under diffeomorphisms and gauge transformations.
TQFT has applications in various areas of physics, including condensed matter physics, quantum gravity, and string theory. In condensed matter physics, TQFT is used to describe the behavior of topological phases of matter, such as topological insulators and superconductors. In quantum gravity, TQFT is used to study the topology of spacetime, and in string theory, TQFT plays an important role in the study of D-branes and their interactions.
Some well-known examples of TQFTs include the Chern-Simons theory, which describes the fractional quantum Hall effect, and the Witten-Reshetikhin-Turaev theory, which is used to compute the Jones polynomial of knots and links.
