Einstein-maxwell null fields and extended massless particles with helicity

The concept of extended elementary particles proposed by the author in previous papers is briefly outlined in a slightly modified form. In this framework special Einstein-Maxwell null fields are interpreted as extended massless particles with helicity. A model of extended photons is proposed.     

Ray helicity: geometric invariant for multidimensional resonant wave conversion

For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning, it must be invariant under the following two groups of transformations, which are used to construct solutions: congruence transformations (which involve linear combinations of components of the multicomponent wave field) and canonical transformations (which act on the ray phase space). It is shown that for conversion between two waves there is a new invariant not previously discussed: the intrinsic helicity of the ray.     

Dimensionally Renormalized Green's functions for theories with massless particles. I

In the framework of dimensional renormalization the existence of Green's functions to all orders of perturbation theory is proved for theories of massless particles without super-renormalizable couplings. For those Green's functions Schwinger's Action Principle holds as in the massive case.     

Dimensionally renormalized Green's functions for theories with massless particles. II

In the framework of dimensional renormalization the existence of Green's functions to all orders of perturbation theory is proved for theories with massless particles, provided all terms in the interaction Lagrangian have infrared degree 4. If the vanishing of masses is enforced by some symmetry and this symmetry is respected by dimensional regularization, Schwinger's action principle holds for these Green's functions as in the massive case.On leave of absence from Max-Planck-Institut für Physik und Astrophysik, D-8000 München, Federal Republic of GermanySupported in part by the National Science Foundation Grant # MPS-74-13208 A01Supported in part by the National Science Foundation Grant # GU 3186     

Distinguishable equivalent particles with symmetrized wave functions

The quantum formalism ofdistinguishable, yetequivalent particles (with symmetric or antisymmetric wave functions) is here worked out. The result is an entirely explicit formulation of the way in which classical mechanics emerges from quantum mechanics for such particles. Distinguishability is achieved at the cost of dynamical precision; the two are, in fact, complementary.Research sponsored in part by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. 557–67.     

Difficulties with massless particles?

Some difficulties with sharp momentum (one-particle) states for massless particles are indicated, in the framework of unitary irreducible representations of the Poincaré group. It is shown that a Poincaré covariant set of such states requires the introduction, in the spatial direction opposite to the point stabilized, of momentum generalized eigenstates which (when the helicity is nonzero) have a nontrivial orbital transformation. The relevance of these generalized momentum eigenstates for massless theories is then shown.     

Fock representation and massless particles

We present some remarks on the representations of Canonical Commutation or Anticommutation Relations which describe free massless particles.On leave from Istituto di Fisica dell'Università, Roma.     

Two particle unitarity for helicity amplitudes with particles of arbitrary spin

The two particle unitarity contribution to the double spectral function of the scattering amplitude for any 2 → 2 process is explicitly calculated for the case of arbitrary spins of the initial, intermediate and final particles. A closed, simple result is obtained which is a generalization of the Mandelstam result for spinless particles. The results should be of value in calculations of the contribution of the exchange of pairs of high spin particles to the nucleon-nucleon force.     

Non-abelian traveling wave solutions for massless QCD2

The field equations for quantum chromodynamics in 1 + 1 dimensions (QCD₂) with massless fermions are shown to admit classical non-abelian traveling wave solutions. In this case, the field equations reduce to the linear Frenet-Serret equations for a curve in the three-space corresponding to an SU(2) subalgebra of the SU(N) gauge group.     

Confinement of massless particles: Photon

Confinement of massless particles in a suitably chosen dielectric medium is considered. Light waves of selected frequencies are shown to be confined in a medium with dielectric constantε(r)=a/r−b ². A wave theoretical analysis gives equispaced frequency spectrum for the confined light, the radial dependence of its electric wave vector resembling that of hydrogen atom wave functions. In the large frequency limit an eikonal approximation of the problem gives elliptic orbits for the confined rays. Higher frequency orbits are shown to be closer to the centre of the medium than the lower frequency ones.