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

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## Abstract

**:**

## 1. Introduction

## 2. Boundary Terms in Coordinate and Momentum Space

## 3. Problems with Relocalization for Gluons

- (i)
- If RI is indeed violated the coupling of nucleons to gravity (described by the formfactors of Belinfante EMT [13,23]) may be unconstrained by the form of conservation laws in terms of canonical EMT. In extreme case, assuming that just the canoncical form is related to translational invariance, this might result in the violation of Equivalence Principle for nucleons at several percent level which may be tested experimentally and is probably already excluded by the data.
- (ii)
- One may assume “Hadronic censorship” leading to the absence of the ghost pole: in this case the matrrix element$$<P,S|{J}_{5}^{\mu}-{K}^{\mu}|P,S>=0$$
- (iii)
- The simplest solution would be the impossibility to separate spin and orbital momenta of gluons in the meaningful way.

## 4. Discussion

- (i)
- investigation of boundary terms in hydrodynamic approximation;
- (ii)
- exploration of the role of boundary terms (spoiling the transition of spin to orbital AM) for twisted states, which might be obtained also at high energies (see [24] and Ref. therein) and provide the complementary description of Transverse Momentum Dependent parton correlators.

## Funding

## Acknowledgments

## Conflicts of Interest

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Teryaev, O.
Energy-Momentum Relocalization, Surface Terms, and Massless Poles in Axial Current Matrix Elements. *Symmetry* **2020**, *12*, 1409.
https://doi.org/10.3390/sym12091409

**AMA Style**

Teryaev O.
Energy-Momentum Relocalization, Surface Terms, and Massless Poles in Axial Current Matrix Elements. *Symmetry*. 2020; 12(9):1409.
https://doi.org/10.3390/sym12091409

**Chicago/Turabian Style**

Teryaev, Oleg.
2020. "Energy-Momentum Relocalization, Surface Terms, and Massless Poles in Axial Current Matrix Elements" *Symmetry* 12, no. 9: 1409.
https://doi.org/10.3390/sym12091409