Chan Hong-Mo

Half-string oscillator approach to string field theory

Abstract We give an operator formulation of the string field theory proposed by E. Witten using half-string oscillator modes. This formalism, identifying the physical string states as infinite matrices, is developed in such a way that interactions at the level of vertices can be calculated in terms of products and traces of these matrices without relying on ill-defined manipulations of functional integrals.

't Hooft's order-disorder parameters and the dual potential

It is shown that the operator B(C) = Tr[P exp ig̃ ∮ Ãi(x)dx ] constructed with the recently derived dual potential Ã(x) and a coupling g̃ related to g by the Dirac quantization condition satisfies the correct commutation relation with the Wilson operator Tr[P exp ig ∮ Ai(x)dx ] as required by ’t Hooft for his order-disorder parameters. chanhm@v2.rl.ac.uk tsou @maths.ox.ac.uk In his study of the confinement problem in nonabelian gauge theories, ’t Hooft introduced 2 loop-dependent operators A(C) and B(C) with the following commutation relations: [1] A(C)B(C ′) = B(C ′)A(C) exp(2πin/N) (1) for su(N) gauge symmetry, and any two spatial loops C and C ′ with linking number n between them. A(C) was explicitly given as: A(C) = Tr [

Circumstantial evidence for rotating mass matrix from fermion mass and mixing data

Abstract. It is shown that existing data on the mixing between up and down fermion states and on the hierarchical mass ratios between fermion generations, as far as can be so analyzed at present, are all consistent with the two phenomena being both consequences of a mass matrix rotating in generation space with changing energy scale. As a result, the rotating mass matrix can be traced over some 14 orders of magnitude in energy from the mass scale of the t quark at 175 GeV to below that of the atmospheric neutrino at 0.05 eV.

On loop space formulation of gauge theories

Abstract In attempting to formulate gauge theories entirely in terms of loop variables, it is found convenient to work in the function space of parametrised loops with the loop space connection F μ (C¦s) as field variables. Equivalence to the conventional formulation in terms of the gauge potential Aμ(x) is ensured by imposing on F μ (C¦s) certain conditions implying the local absence of “magnetic sources” or monopoles. These conditions are reminiscent of the Poincare lemma in electromagnetism, and establish a one-one correspondence between F μ (C¦s) so constrained and Aμ(x) up to gauge equivalence. We use this approach to reformulate the action principle for pure gauge theories and to derive field equations from it completely in terms of loop variables. We believe that the formalism is useful in the theory of monopoles and may also find application in lattice calculations.

Neutrino oscillations in the dualized standard model

A method developed from the dualized standard model for calculating the quark CKM matrix and masses is applied to the parallel problem in neutrino oscillations. Taking the parameters determined from quarks and the masses of two neutrinos:

Flavor changing neutral currents in the dualized standard model

{m}_{3}^{2}\ensuremath{\sim}{10}^{\ensuremath{-}2}\char21{}{10}^{\ensuremath{-}3} {\mathrm{eV}}^{2}

Action principle and equations of motion for nonabelian monopoles

suggested by atmospheric neutrino data and

On the corner elements of the CKM and PMNS matrices

{m}_{2}^{2}\ensuremath{\sim}{10}^{\ensuremath{-}10} {\mathrm{eV}}^{2}

Towards a “pointless” generalisation of Yang-Mills theory

suggested by the long-wavelength oscillation solution of the solar neutrino problem, one obtains from a parameter-free calculation all the mixing angles in reasonable agreement with existing experiments. However, the scheme is found not to accommodate comfortably the mass values

Phototransmutation of leptons

{m}_{2}^{2}\ensuremath{\sim}{10}^{\ensuremath{-}5} {\mathrm{eV}}^{2}