Energy-Momentum Relocalization, Surface Terms, and Massless Poles in Axial Current Matrix Elements

Oleg Teryaev

doi:10.3390/sym12091409

Abstract

The energy-momentum relocalization in classical and quantum theory is addressed with specific impact on non-perturbative QCD and hadronic structure. The relocalization is manifested in the existence of canonical and symmetric (Belinfante and Hilbert) energy momentum tensors (EMT). The latter describes the interactions of hadrons with classical gravity and inertia. Canonical EMT, in turn, is naturally emerging due to the translation invariance symmetry and appears when spin structure of hadrons is considered. Its relation to symmetric Hilbert and Belinfante EMTs requires the possibility to neglect the contribution of boundary terms for the classical fields. For the case of quantum fields this property corresponds to the absence of zero-momentum poles of matrix element of the axial current dual to the spin density. This property is satisfied for quarks manifesting the symmetry counterpart of UA(1) problem and may be violated for gluons due to QCD ghost pole.

Highlights

The space-time symmetry related to the energy-momentum and angular momentum conservation is manifested in field theory as the appearance of energy-momentum and spin currents
The interaction of particles with gravity involves the symmetruc Hilbert tensor resulting from the variation with respect to metric and the symmetry property naturally emerges after the absorption of spin density to the orbital one using the Belinfante procedure [1]
The interplay of both forms of Energy-Momentum Tensor (EMT) is especially important for hadrons, as in the absence of mathematically rigorous confinement theory their spin structure is an important problem of non-perturbative Quantum Chromodynamics (QCD)

Summary

Introduction

The space-time symmetry related to the energy-momentum and angular momentum conservation is manifested in field theory as the appearance of energy-momentum and spin currents The interaction of particles with gravity involves the symmetruc Hilbert tensor resulting from the variation with respect to metric and the symmetry property naturally emerges after the absorption of spin density to the orbital one using the Belinfante procedure [1]. The interplay of both forms of Energy-Momentum Tensor (EMT) is especially important for hadrons, as in the absence of mathematically rigorous confinement theory their spin structure is an important problem of non-perturbative Quantum Chromodynamics (QCD).

Boundary Terms in Coordinate and Momentum Space

Problems with Relocalization for Gluons

Discussion