Some global properties of massless free fields

Elementary group-theoretical considerations show that global solutions to the massless free field equations are functions on the bundle of twistor dyads, rather than the bundle of conformal spin frames. Only in certain degenerate cases may they be thought of as ordinary spinor fields. This is the origin of the Grgin discontinuity.Supported in part by the University of Kansas Research Fund and by the Science Research Council     

New twistorial integral formulas for massless free fields of arbitrary spin

A manifestly scaling-invariant version of the Kirchoff-D'Adhemar-Penrose field integrals is presented. The invariant integral expressions for the spinning massless free fields are directly transcribed into the framework of twistor theory. It is then shown that the resulting twistorial field integrals can be thought of as being equivalent to the universal Penrose contour integral formulas for these fields.     

Light-cone quantization for massless fields

When the light-cone quantization procedure is applied to massless fields care must be taken or the resulting theory will not be isomorphic to the equivalent theory quantized at equal times. The special considerations necessary for massless fields are described here and their application to recently presented calculations in 1+1 dimensions are discussed.     

Twistor integral representations of fundamental solutions of massless field equations

We consider the general dimensional (complex) Minkowski spaces and the extended twistor spaces. We show that the fundamental solutions of the complex wave or Laplace equations are explicitly represented by the integrals of some closed forms on the twistor spaces. The closed form is defined from labeled trees explained in graphs theory, and is written, as the cohomology class, by the linear combination of the logrithmic forms on some hyperplane configuration complement in some complex affine space.     

Boundary terms for massless fermionic fields

Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal _e n _A/A to the boundary and a pair of independent spinor fields ^A and . This paper studies the corresponding classical properties, i.e., the classical boundary-value problem and boundary terms in the variational problem. If is set to zero on a 3-sphere bounding flat Euclidean 4-space, the modes of the massless spin–1/2 field multiplying harmonics having positive eigenvalues for the intrinsic 3-dimensional Dirac operator onS ³ should vanish onS ³. Remarkably, this coincides with the property of the classical boundary-value problem when spectral boundary conditions are imposed onS ³ in the massless case. Moreover, the boundary term in the action functional is proportional to the integral on the boundary of ^A _e n _AA ^A .     

A generalized consistency condition for massless fields

Using a generalized consistency condition (gcc), we construct couplings between massless scalar fields and the spin 2 gravitational field. Specifically, we consider all possible third-order interaction terms for scalar fields and a and use the gcc to single out one. We also find three generalized current identities associated with the massless gauge fields.     

On the nuclearity condition for massless fields

It is shown that quantum field theories of free massless particles satisfy a recently proposed nuclearity condition restricting the admissible number of local degrees of freedom of a theory. This result is based on an improved bound for the nuclearity index of certain specific sets of vectors in Fock space.     

Quantum theory of a massless spinning particle

The classical and quantum mechanics of a free massless point-like fermion is presented. The action is invariant under local 1-dimensional reparametrizations and supersymmetry, as well as a large set of rigid symmetries, including conformal and chiral symmetries. An infinite set of rigid symmetries is derived starting from the chiral invariance, but only a finite subset does not vanish on shell. The BRST-transformations corresponding to thed=1 local symmetries are constructed and the quantization is performed. Finally, the BRST-cohomology is investigated and the conditions producing the physical states are derived.     

Twistor diagram equalities for generalized mass-scattering integrals for Dirac fields

A method which enables one to convert the integral of a holomorphic projective twistor one-form into the integral of a holomorphic projective twistor three-form is used to modify the end-vertex structures of certain twistor diagrams that represent mass-scattering integrals for Dirac fields. Each term of the twistorial diagrammatic expansions recovering the entire fields is then re-expressed appropriately. This gives rise to four sets of explicit twistor-diagram equalities for the mass-scattering formulae.I am most grateful to Professor Roger Penrose for making a key point concerning the introduction of the basic auxiliary-twistor vertices. My warmest thanks go to the World Laboratory for supporting this work financially. I wish to acknowledge the Third World Academy of Sciences for a relevant travel grant. I am grateful, also, to Dr. Asghar Quadir for his invaluable suggestions.     

Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.     

New exact Einstein-Maxwell fields for a massless charge

New solutions of the Einstein-Maxwell equations are presented. The solutions describe the gravitational fields of a massless charge.     

Unfolded equations for current interactions of 4d massless fields as a free system in mixed dimensions

Journal of Experimental and Theoretical Physics - Interactions of massless fields of all spins in four dimensions with currents of any spin are shown to result from a solution of the linear problem...