We present a pedagogical approach to the Lorentz group. We start by introducing a compact notation to express the elements of the fundamental representation of the rotations group. Lorentz coordinate transformations are derived in a novel and compact form. We show how to make a Lorentz transformation on the electromagnetic fields as well. A covariant time-derivative is introduced in order to de...

We show that under the operation of parity the front-form (1/2, 0) and (0, 1/2) Weyl spinors (massive or massless) do not get interchanged. This has the important consequence that if a frontform theory containing (1/2, 0)⊕ (0, 1/2) representation space has to be parity covariant then one must study the evolution of a physical system not only along x but also along the x direction. As a result o...

Recently, Sahlmann [1] proposed a new, algebraic point of view on the loop quantization. He brought up the issue of a ⋆-algebra underlying that framework, studied the algebra consisting of the fluxes and holonomies and characterized its representations. We define the diffeomorphism covariance of a representation of the Sahlmann algebra and study the diffeomorphism covariant representations. We ...

The vector and axial pion-photon transition distribution amplitudes are analyzed in the Spectral Quark Model. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the α representation of propagators. As a result polynomiality is incorporated and calculations become rather simple. Explicit formulas, holding at the low-energy quark-mo...

Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of cross product C-algebras C0(X)⋊G coming from covariant pairs. Here G is assumed countable, X a manifold, and X ⋊ G cocompact and proper. The formula in question expresses the graded trace of the map on rationalized K-theory of C0(X) ⋊G induced by the endomorphism, i.e. the Lefschetz numbe...

We give a new representation as tempered distribution for the energy–momentum tensor of a system of charged point–particles, which is free from divergent self– interactions, manifestly Lorentz–invariant and symmetric, and conserved. We present a covariant action for this system, that gives rise to the known Lorentz–Dirac equations for the particles and entails, via Noether theorem, this energy–...

Equations of coupled electron–nuclear dynamics (CEND) that describe molecular dynamics within a fully classical approach have been derived. Utilization of the language of fiber bundles and connections (gauge fields) allows one to represent the resulting classical Hamilton equations in an invariant (coordinate-covariant) form. Applications of the CEND equations to calculations of off-resonant no...

The reduced covariant phase space associated with the three-dimensional Euclidean Nambu-Goto action can be identified, via the Enneper-Weierstrass representation of minimal surfaces, with the space of complex analytic functions plus three translational zero modes. The symplectic structure induced trough the Enneper-Weierstrass map can be explicitly computed. Quantization is then straightforward...

The coherent states associated to the discrete series representations D(Eo, s) of SO(3, 2) are constructed in terms of (spin-)tensor fields on D = 4 anti-de Sitter space. For Eo > s + 5 the linear space HEo,s spanned by these states is proved to carry the unitary irreducible representation D(Eo, s). The SO(3, 2)-covariant generalized Fourier transform in this space is exhibited. The quasiclassi...

We study the pion electromagnetic and γ + π0 → γ transition form factors at intermediate momentum transfer. We calculate soft, nonperturbative corrections to the leading perturbative amplitudes which arise from the qq̄component of the pion wave function. We work in Minkowski space and use a Lorentz covariant, gauge-invariant generalized perturbative integral representation for the qq̄ amplitudes....