Mark G. Mitchard

The chiral Ward-Takahashi identity in the ladder approximation

Abstract We show that the ladder approximation to the Schwinger-Dyson and Bethe-Salpeter equations preserves the Ward-Takahashi identity for the axial vector vertex if and only if we use the gluon momentum as the argument of the running coupling constant. However, in the usual Landau gauge this is inconsistent with the vector Ward identity. We propose a new method for making the ladder approximation scheme consistent with both vector and axial vector Ward identities.

Meson properties from the ladder Bethe-Salpeter equation

Abstract Working in the improved ladder approximation to QCD, we calculate the two point correlation functions for the composite operators ψ Mψ . From these we extract mass values and decay constants for the lowest lying scalar, vector and axial vector mesons. Considering the naivety of the approximation used, and that we have no free parameters once the QCD scale is set, the results are surprisingly good.

Calculating fπ in the consistent ladder approximation

Abstract We recalculate the pion decay constant ƒ π and the vacuum expectation value 〈 ψ ψ〉 in a new ladder approximation scheme to the Schwinger-Dyson and Bethe-Salpeter equations which is consistent both with the axial Ward-Takahashi identity and Z2 = 1 condition (or the vector Ward identity in the abelian case). We find that our previous numerical results remain qualitatively unchanged: in particular, the Pagels-Stokar formula is a good approximation to ƒ π which agrees with the ladder-exact value to within 5%–30%.

A heteropolymer model study for the mechanism of protein folding

A heteropolymer model of randomly self-interacting chains in two dimensions is studied with numerical simulations in order to elucidate the folding mechanism of protein. We find that the model occasionally shows folding propensity depending on the sequence of random numbers given to the chain. We study the thermodynamic and kinematic roles in the folding mechanism by grouping the local energy minima found in the simulations into clusters according to the similarity of their conformations. It is suggested that the local minima to which some heteropolymers show a folding tendency are always the lowest energy states of the energy spectrum within a cluster, though which cluster is selected depends on the sequence. For the eight random sequences we study, we find that the energy gap between the ground state and excited states is little correlated with folding or nonfolding. We rather find that folding propensities are correlated with the global structure of the average energy surface, implying a dominant kinetic role in the folding mechanism, although thermal factors cannot be ignored as the mechanism of choosing the ground state within a cluster of states connected by small deformations. We suggest that a hierarchical cluster structure plays an important role in selecting a unique folded state out of the huge number of local minima of heteropolymers.

Energy level structure of two-dimensional self-interacting random chains

The authors study the energy level structure of the lowest-lying states for a two-dimensional version of the random chain model proposed by Iori, Marinari and Parisi (1991). The authors find that the multifold degeneracy of the ground state is lifted as the random noise interaction is switched on and a solitary global minimum emerges in a glassy phase as the strength of the noise term is increased. This indicates that the model mimics the characteristics expected of a native protein. They also show that the transition from the globule state (with no noise term) to the glassy phase takes place smoothly.

Self Interacting Random Chains

We analyse a simple continuum model of self interacting chains in 2-dimensions to show that it contains certain essential features of protein folding. In particular we observe, for folding sequences, sequential folding proceeding through a globule phase before making the folding transition.