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Title: Angular momentum conservation law in light-front quantum field theory

Abstract

We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that j 3, the z -component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j 3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.

Authors:
 [1];  [1]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1360755
Alternate Identifier(s):
OSTI ID: 1349545
Grant/Contract Number:
AC02-76SF00515
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 95; Journal Issue: 6; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Chiu, Kelly Yu-Ju, and Brodsky, Stanley J. Angular momentum conservation law in light-front quantum field theory. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.95.065035.
Chiu, Kelly Yu-Ju, & Brodsky, Stanley J. Angular momentum conservation law in light-front quantum field theory. United States. doi:10.1103/PhysRevD.95.065035.
Chiu, Kelly Yu-Ju, and Brodsky, Stanley J. Fri . "Angular momentum conservation law in light-front quantum field theory". United States. doi:10.1103/PhysRevD.95.065035. https://www.osti.gov/servlets/purl/1360755.
@article{osti_1360755,
title = {Angular momentum conservation law in light-front quantum field theory},
author = {Chiu, Kelly Yu-Ju and Brodsky, Stanley J.},
abstractNote = {We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that j3, the z -component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.},
doi = {10.1103/PhysRevD.95.065035},
journal = {Physical Review D},
number = 6,
volume = 95,
place = {United States},
year = {Fri Mar 31 00:00:00 EDT 2017},
month = {Fri Mar 31 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
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Citation Metrics:
Cited by: 4works
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  • We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that j 3 , the z -component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j 3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QEDmore » and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.« less
  • Cited by 4
  • It is shown that if conservation of the z-component of the angular momentum during multiple meson production is taken into account by the simplest classical way, the predictions of the statistical theory remain almost unchanged. The anisotropy in the angular distribution of the particles which thus appears is apparently smaller than that observed in reality. (auth)
  • The role of the Leutwyler and Stern spin operator in the angular momentum analysis of light-front scattering theory is analyzed. The equations of formal scattering theory are transformed to the {xi} picture using the unitary operator {ital C}({xi}) recently developed by the author. This operator depends on the two angles which determine the direction of the three-vector part of a lightlike four-vector {xi}. It is shown that an invariant version of light-front perturbation theory developed earlier by the author is related to the standard theory by the unitary operator {ital C}({xi}). It is also shown how to carry out amore » partial-wave analysis of the Lippmann-Schwinger-like equations obtained by summing a subset of the diagrams of this invariant form of light-front perturbation theory. The analysis presented here makes clear that the {xi} picture overcomes many of the difficulties due to the interaction dependence of light-front angular momentum operators, in particular the difficulties arising from the fact that the individual diagrams of light-front pertubation theory are not rotationally invariant.« less
  • A quantum-field-theory approach is put forward to generalize the concept of classical spatial light beams carrying orbital angular momentum to the single-photon level. This quantization framework is carried out both in the paraxial and nonparaxial regimes. Upon extension to the optical phase space, closed-form expressions are found for a photon Wigner representation describing transformations on the orbital Poincare sphere of unitarily related families of paraxial spatial modes.