Hsien Chung Kao

Noncommutative quantum mechanics from noncommutative quantum field theory.

We derive noncommutative multiparticle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Particles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously and propose a way to construct noncommutative SU(5) grand unified theory.

The Chern-Simons coefficient in supersymmetric Yang-Mills Chern-Simons theories

Abstract We study one-loop corrections to the Chern-Simons coefficient κ = k 4π in N = 1, 2, 3 supersymmetric Yang-Mills Chern-Simons systems. In the pure bosonic case, the shift of the parameter k is known to be k → k + cv, where cv is the quadratic Casimir of the gauge group. In the N = 1 case, the fermionic contribution cancels the bosonic contribution by half and the shift is k → k + c v 2 , making the theory anomalous if cv is odd. In the N = 2, 3 cases, the fermionic contribution cancels the bosonic contribution completely and there is no correction. We also calculate the mass corrections, and show that the supersymmetry is preserved. As the matter fields decouple from the gauge field in the pure Chern-Simons limit, this work sheds some light on the regularization dependency of the correction in pure Chern-Simons systems. We also discuss the implication to the case when the gauge symmetry is spontaneously broken by the Higgs mechanism.

Self-dual Chern-Simons Higgs systems with an N=3 extended supersymmetry.

We construct and study an {ital N}=3 supersymmetric Chern-Simons Higgs theory. This theory is the maximally supersymmetric one containing the self-dual models with a single gauge field and no gravity.

Self-dual SU(3) Chern-Simons Higgs systems

We explore self-dual Chern-Simons Higgs systems with the local SU(3) and global U(1) symmetries where the matter field lies in the adjoint representation. We show that there are three degenerate vacua of different symmetries and study the unbroken symmetry and the particle spectrum in each vacuum. We classify the self-dual configurations into three types and study their properties.

BPS domain wall solutions in self-dual Chern-Simons-Higgs systems

We study domain wall solitons in the relativistic self-dual Chern-Simons-Higgs systems by the dimensional reduction method to two-dimensional spacetime. The Bogomol{close_quote}nyi bound on the energy is given by two conserved quantities in a similar way that the energy bound for Bogomol{close_quote}nyi-Prasad-Sommerfield (BPS) dyons is set in some Yang-Mills-Higgs systems in four dimensions. We find the explicit soliton configurations which saturate the energy bound and their nonrelativistic counterparts. We also discuss the underlying N=2 supersymmetry. {copyright} {ital 1997} {ital The American Physical Society}

The Chern-Simons coefficient in the Higgs phase

Abstract We study one-loop corrections to the Chern-Simons coefficient ϰ in abelian self-dual Chern-Simons Higgs systems and their N=2 and N=3 supersymmetric generalizations in both symmetric and asymmetric phases. One-loop corrections to the Chern-Simons coefficient of these systems turn out to be integer multiples of 1 4 π in both phases. Especially in the maximally supersymmetric N=3 case, the correction in the symmetric phase vanishes and that in the asymmetric phase is ϰ/(2π|ϰ|). Our results suggest that nonabelian self-dual system might enjoy similar features. We also discuss various issues arising from our results.

Quantum nucleation of vortex string loops.

We investigate quantum nucleation of vortex string loops in the relativistic quantum field theory of a complex scalar field by using the Euclidean path integral. Our initial metastable homogeneous field dominated by the

Binding transition in quantum hall edge states

O(3)

Mass spectra of N = 2 supersymmetric SU(n) Chern-Simons-Higgs theories

symmetric bounce solution. The nucleation rate and the critical vortex loop size are obtained approximately. Gradually the initial current will be reduced to zero as the induced current inside vortex loops is opposite to the initial current. We also discuss a similar process in Maxwell-Higgs systems and possible physical implications.

Chern-Simons coefficient in supersymmetric non-Abelian Chern-Simons Higgs theories

We study a class of Abelian quantum Hall (QH) states which are topologically unstable (T-unstable). We find that the T-unstable QH states can have a phase transition on the edge which causes a binding between electrons and reduces the number of gapless edge branches. After the binding transition, the single-electron tunneling into the edge gains a finite energy gap, and only certain multi-electron co-tunneling (such as three-electron co-tunneling for