We review quantum field theory approach to the knot theory. Using holomorphic gauge we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental results and temporal gauge considerations which lead to representation of Vassiliev invariants in terms of arrow diagrams. Explicit examples and computational results are presented
We study the 2D massive fields in the presence of moving mirrors. We do that for standing mirror and mirror moving with constant velocity. We calculate the modes and commutation relations of the field operator with the corresponding conjugate momentum in each case. We find that in case of the ideal mirror, which reflects modes with all momenta equally well, the commutation relations do not have their canonical form. However, in the case of nonideal mirror, which is transparent for the modes with high enough momenta, the commutation relations of the field operator and its conjugate momentum have their canonical form. Then, we calculate the free Hamiltonian and the expectation value of the stress-energy tensor in all the listed situations. In the presence of moving mirrors the diagonal form in terms of the creation and annihilation operators has the operator that performs translations along the mirror’s worldline rather than the one which does translations along the time-line. For the massive fields in the presence of a mirror moving with constant velocity the expectation value of the stress-energy tensor has a nondiagonal contribution which decays with the distance from the mirror.
Neutron stars contain superdense matter in their interiors. Characteristic densities in their cores are several times higher than the standard density of nuclear matter. This matter is so dense that it would be natural to assume that frequent particle collisions produce immediate equilibration. However, because of the slowness of some reactions, the equilibration with respect to them can be greatly delayed. Then one should deal with non-equilibrium stars which contain extra energy to be released. Deviations from equilibrium can affect neutrino emission of neutron stars, warm up their interiors and influence their thermal evolution. The effects of equilibration can be important for pulsating, rotating, accreting neutron stars, as well as for merging binary neutron stars.
We propose an explicit construction for the integrable models on Poisson submanifolds of the Lie groups. The integrals of motion are computed in cluster variables via the Lax map. This generalized construction for the co-extended loop groups allows to formulate, in general terms, some new classes of integrable models.
We present a simple and general procedure for calculating the thermal radiation coming from any stationary metric. The physical picture is that the radiation arises as the quasi–classical tunneling of particles through a gravitational barrier. We study three cases in detail: the linear accelerating observer (Unruh radiation), the non-rotating black hole (Hawking radiation), and the rotating/orbiting observer (circular Unruh radiation). For the linear accelerating observer we obtain a thermal spectrum with the usual Unruh temperature. For the non-rotating black hole we obtain a thermal spectrum, but with a temperature twice that given by the original Hawking calculations. We discuss possible reasons for the discrepancies in temperatures as given by the two different methods. For the rotating/orbiting case the quasi–classical tunneling approach indicates that there is no thermal radiation. This result for the rotating/orbiting case has experimental implications for the experimental detection of this effect via the polarization of particles in storage rings.
Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is described by the degeneration of the twisted WZW model on elliptic curves. The spaces of conformal blocks and conformal coinvariants of the degenerate model are factorised into those of the orbifold WZW model.