Ingemar Bengtsson

Cubic interaction terms for arbitrary spin

Abstract Using the light-cone formulation of dynamics, we construct cubic self-interaction terms for massless fields of arbitrary helicity λ. The coupling constants have dimension [length]λ−1 and there is a gauge group for any odd λ.

Cubic interaction terms for arbitrarily extended supermultiplets

Abstract Using a light-cone superspace formalism we construct cubic interaction terms for all maximally extended supersymmetry multiplets where the maximum helicity λ is an integer. The coupling constants have dimension [length]λ−1 and there is a gauge group for any odd λ.

Particles, twistors and the division algebras

We study twistorial mechanics of particles and super-particles in six dimensions. To this end we formulate (in a general division algebra framework) a twistor theory in D = 6 based on quaternionic numbers, and prove the equivalence between this version of particle dynamics and the ordinary one. The super-twistors define a covariant and gauge invariant concept of a super world-line and allow us to write an action for the supersymmetric particle that is not plagued by the content of second class constraints that prevents a covariant quantization in the space-time picture. The notion and geometry of projectile twistor space, and its connection to Minkowski space, are examined and shown to directly generalize the results in D = 3, 4. Quantization is performed and analytic quaternionic eigenfunctions and integrations are discussed. We also draw some conclusions on the possible generalization to ten dimensions.

On Chiral p-Forms

Some aspects of chiral p-forms, in particular the obstruction that makes it hard to define covariant Green functions, are discussed. It is shown that a proposed resolution involving an infinite set of gauge fields can be made mathematically rigorous in the classical case. We also give a brief demonstration of species doubling for chiral bosons.

The cosmological constants

Abstract We point out that the lagrangian due to Capovilla, Jacobson and Dell, as well as the hamiltonian due to Ashtekar, both of which describe complex four dimensional general relativity, permit the introduction of an infinite set of parameters, one of which is the usual cosmological constant. For arbitrary choices of the parameters, the model has two degrees of freedom, and we show how to identify the space-time metric in terms of them. The connection between the lagrangian and the hamiltonian is partially worked out.

Yang-Mills theory and general relativity in three and four dimensions

Abstract Ashtekar has shown that general relativity can be “embedded” in the phase space of a Yang-Mills theory with a rank one gauge algebra, provided that the dimension of space is three. Witten has given a similar construction, valid when the dimension of space is two. In this letter we show how these two results are related to each other. In fact, Ashtekars formulation works also in the lower dimension, and it is equivalent to Wittens formulation as long as the spatial metric is non-degenerate. We explain why a simplified constraint algebra appears in the latter case.

Manifest Duality in Born–Infeld Theory

Born–Infeld theory is formulated using an infinite set of gauge fields, along the lines of McClain, Wu and Yu. In this formulation electromagnetic duality is generated by a fully local functional. The resulting consistency problems are analyzed and the formulation is shown to be consistent.

Ashtekar's variables, the θ-term, and the cosmological constant

Abstract Capovilla, Jacobson and Dell have given a lagrangian for pure gravity in which only an SO(3) connection and a Lagrange multiplier appears. We show that the introduction of a cosmological constant leads to a non-polynomial action, which we determine to tenth order in the curvature. We point out that, in Ashtekars hamiltonian formulation, the cosmological constant can be introduced by a transformation that is formally similar to the transformation which leads to a θ-term.

ANOTHER “COSMOLOGICAL” CONSTANT

Capovilla, Jacobson and Dell have found a one-parameter family of field equations which coincides with Einstein’s equations when the parameter is set to zero. The basic variable is an SO(3) vector potential. For generic values of the parameter, we show that the solutions of the field equations may be interpreted in terms of Riemannian geometry. The space-time metric is expressible in terms of the field strengths. The connection between the SO(3) fibers and the tangent space of space-time is not that of the tetrad formalism. The metric is not Ricci flat. Coupling to a massless scalar field is given as an example of matter couplings. Spherically symmetric solutions are given. In the nonrelativistic limit there is a deviation from Newton’s inverse square law, and this is used to set an observational bound on the parameter.

Remarks on topological brane theories

We consider the theory of closed