arXiv subjects
Publications and source records attributed to Seungjoon Hyun.
We study the twisted $N=2$ supersymmetric Yang-Mills theory coupled with the hypermultiplets (TQCD). We suggest that the family of TQCD can be served as a powerful tool for studying the quantum field theoretic properties of the underlying physical theories.
We study the path integrals of the holomorphic Yang-Mills theory on compact Kähler surface with $b_2^+ = 1$. Based on the results, we examine the correlation functions of the topological Yang-Mills theory and the corresponding Donaldson invariants as well as their transition formulas.
Covariantly we reformulate the description of a spinning particle in terms of the Poincaré group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the Lagrangian. Furthermore, in this covariant reformulation, the Lorentz element is to be considered to evolve the momentum or spin component from an arbitrary fixed frame and not just from the particle rest frame. In distinction with the usual formulation, our system is directly comparable with the pseudo-classical formulation. We get a peculiar symmetry which resembles the supersymmetry of the pseudo-classical formulation.
For the `classical' formulation of a massive spinning particle, the propagator is obtained along with the spin factor. We treat the system with two kinds of constraints that were recently shown to be concerned with the reparametrization invariance and `quasi-supersymmetry'. In the path integral, the BRST invariant Lagrangian is used and the same spin factor is obtained as in the pseudo-classical formulation.
The spin degrees of freedom for the relativistic particle are described by either Poincaré group variables (classically) or Grassmann variables (pseudo-classically). The relationship between those two descriptions are given. In doing that, appropriate constraints are constructed to put into the lagrangian. Especially a natural relation of Poincaré group variables and Grassmann variables is obtained. Hopf fibration relating the spin momentum to the group is just the right transformation of the spin momentum under Poincaré group. And with the relation just mentioned, pseudoclassical lagrangian is derived naturally from the classical one.