arXiv subjects
Publications and source records attributed to Min Chul Lee.
This paper extends the notion of Schwinger functions to quantum Yang-Mills theories and proposes the axioms they should satisfy. Two main features of this axiom scheme are that we assume existence of gauge-invariant co-located Schwinger functions and impose physical properties only on them. This is in accordance with the fundamental principle of gauge theories that only gauge-invariant quantities can be physical observables.
We construct several quantum gauge theories in 4 dimensional space time, including both Abelian and non Abelian gauge groups, with the Abelian gauge fields coupled to zero mass matter fields. The construction occurs in a fixed finite Euclidean spatial domain. The construction begins with the doubly cutoff bare field theory (with a finite space time volume and a mesh based ultraviolet cutoff) constructed in a separate paper. We use a limited range of renormalized perturbation theory, just sufficient to cancel all the divergences. We demonstrate convergence of the ultraviolet limit and of the renormalized perturbation theory, when summed to all orders. We construct the fully renormalized Lagrangian and Schwinger functions.
This paper presents the axioms for a quantum Yang-Mills theory in the Minkowski spacetime. There are two routes of analytic continuation for the Schwinger functions, namely the Wightman functions and time-ordered products of field operators. We check consistency of these two axiom schemes and reproduce some known existing results, including the indefinite metric and BV formalisms.
The mean of Young measure solutions for the Navier-Stokes equations with general initial conditions are PDE solutions of the Navier-Stokes equation of the class considered by Leray and Hopf.
It is shown that a weak solution with monotone-decreasing kinetic energy satisfies the strong energy inequality. Using this criterion, we analyze the behavior with respect to time for all weak solutions without any further assumption on regularity.