Curtis G. Callan

A new improved energy-momentum tensor

Abstract We show that the matrix elements of the conventional symmetric energy-momentum tensor are cut-off dependent in renormalized perturbation theory for most renormalizable field theories. However, we argue that, for any renormalizable field theory, it is possible to construct a new energy-momentum tensor, such that the new tensor defines the same four-momentum and Lorentz generators as the conventional tensor, and, further, has finite matrix elements in every order of renormalized perturbation theory. (“Finite” means independent of the cut-off in the limit of large cut-off.) We explicitly construct this tensor in the most general case. The new tensor is an improvement over the old for another reason: the currents associated with scale transformations and conformal transformations have very simple expressions in terms of the new tensor, rather than the very complicated ones they have in terms of the old. We also show how to alter general relativity in such a way that the new tensor becomes the source of the gravitational field, and demonstrate that the new gravitation theory obtained in this way meets all the epxerimental tests that have been applied to general relativity.

On geometric entropy

Abstract We show that a geometrical notion of entropy, definable in flat space, governs the first quantum correction to the Bekenstein-Hawking black hole entropy. We describe two methods for calculating this entropy - a straightforward Hamiltonian approach, and a less direct but more powerful Euclidean (heat kernel) method. The entropy diverges in quantum field theory in the absence of an ultraviolet cutoff. Various related finite quantities can be extracted with further work. We briefly discuss the corresponding question in string theory.

Exact solution of a boundary conformal field theory

Abstract We study the conformal field theory of a free massless scalar field living on the half-line with interactions introduced via a periodic potential at the boundary. An SU(2) current algebra underlies this system and the interacting boundary state is given by a global SU(2) rotation of the left-moving fields in the zero-potential (Neumann) boundary state. As the potential strength varies from zero to infinity, the boundary state interpolates between the Neumann and the Dirichlet values. The full S-matrix for scattering from the boundary, with arbitrary particle production, is explicitly computed. To maintain unitarity, it is necessary to attribute a hidden discrete “soliton” degree of freedom to the boundary. The same unitarity puzzle occurs in the Kondo problem, and we anticipate a similar solution.

Instantons and massless fermions in two dimensions

The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.

Data mining and the human genome

Abstract : As genomics research moves from an era of data acquisition to one of both acquisition and interpretation, new methods are required for organizing and prioritizing the data. These methods would allow an initial level of data analysis to be carried out before committing resources to a particular genetic locus. This JASON study sought to delineate the main problems that must be faced in bioinformatics and to identify information technologies that can help to overcome those problems. While the current influx of data greatly exceeds what biologists have experienced in the past, other scientific disciplines and the commercial sector have been handling much larger datasets for many years. Powerful data mining techniques have been developed in other fields that, with appropriate modification, could be applied to the biological sciences.