Theory Of Massless Particles Research Articles

The 2(2S + 1)-formalism and its connection with other descriptions

In the framework of the Joos–Weinberg [Formula: see text]-theory for massless particles, the dynamical invariants have been derived from the Lagrangian density which is considered to be a 4-vector. A la Majorana interpretation of the 6-component “spinors”, the field operators of [Formula: see text] particles, as the left- and right-circularly polarized radiation, leads us to the conserved quantities which are analogous to those obtained by Lipkin and Sudbery. The scalar Lagrangian of the Joos–Weinberg theory is shown to be equivalent to the Lagrangian of a free massless field, introduced by Hayashi. As a consequence of a new “gauge” invariance this skew-symmetric field describes physical particles with the longitudinal components only. The interaction of the spinor field with the Weinberg’s [Formula: see text]-component massless field is considered. New interpretation of the Weinberg field function is proposed.

FACTORIZATION IN EXCLUSIVE AND SEMI-INCLUSIVE HEAVY FLAVOR DECAYS AND EFFECTIVE THEORIES FOR MASSLESS PARTICLES

We prove factorization in the semi-inclusive decay B → D(*) + jet using the Large Energy Effective Theory (LEET). It is also shown that the LEET is unable to consistently describe exclusive processes, such as the decay B → D(*) + π(ρ), and therefore also related properties such as factorization. The reason is an oversimplification of transverse momentum dynamics. We present a variant of the LEET, i.e. a new effective theory for massless particles, the [Formula: see text], which properly takes into account transverse momentum dynamics and is the natural framework to study exclusive nonleptonic decays. The transition from the LEET to the [Formula: see text] is analogous to the replacement of geometrical optics with physical optics, the latter taking into account diffraction to a first approximation. A qualitative argument is presented in favor of factorization in the exclusive nonleptonic decays using the [Formula: see text]. Finally, it is shown that the collinear instability of the LEET disappears when semi-inclusive observables are considered.

Chiral (γ5) symmetry of massless fields and neutrino theory of photons

It is shown that the field theory of massless particles has the internal symmetry groupG=U(1) ⊗ AutU(1). The γ5 and dual transformations of neutrino and electromagnetic fields are particular cases of the transformations of this group. TheCP transformations of massless field can also be included in the transformations of this group. The following formulation of Pryce (1938) theorem is given: Statistical properties of the composite photon in the neutrino theory of light are inconsistent with chiral (γ5) symmetry of neutrino and electromagnetic fields.

Positive definite particle densities for the positive frequency solutions of the klein gordon equation with arbitrary mass

In this paper it is shown that the set of kernels introduced previously by Gerlach, Gromes and Petzold can be enlarged considerably. The paper concludes with a remark on the theory of massless particles.

E2 ¯ − Parametrization of SL(2, C)

We consider the E2¯−parametrization of unimodular 2 × 2 matrices A ∈ SL(2, C), which is of the form A=E1e−12aσ3VE2, with V=e12iπσ2 and E=(e−12iφ0ze12iφ)∈E2¯. E2¯ is a covering of the group of Euclidean motions in the plane. We compute the correspondingly factorized matrix elements of the unitary representations of SL(2, C) in an E2¯−basis the result is given in Eq. (6). As a fringe benefit we obtain an integral transform which amounts to expansion in terms of Meijer G-functions and which generalizes the familiar Hankel transform. The results of this paper are useful, e.g., for computing vertex functions in the theory of massless particles with continuous spin.