The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. Interestingly, the construction can be generalized beyond the standard symmetry transformations that leave the action invariant. We also discuss an extended set of transformations, which change the action by a term that is locally known on the level of the quantum effective action. Associated to such extended gauge transformations are currents for which we obtain a divergence-type equation of motion, but they are not conserved. We call them nonconserved Noether currents. We discuss, in particular, symmetries and extended transformations associated to space-time geometry for relativistic quantum field theories. These encompass local dilatations or Weyl gauge transformation, local Lorentz transformations, and local shear transformations. Together they constitute the symmetry group of the frame bundle GL(d). The corresponding nonconserved Noether currents are the dilatation or Weyl current, the spin current, and the shear current. In particular, for the latter, we obtain a new divergence-type equation of motion.

Conserved and nonconserved Noether currents from the quantum effective action / Floerchinger S.; Grossi E.. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - STAMPA. - 105:(2022), pp. 085015.0-085015.1. [10.1103/PhysRevD.105.085015]

Conserved and nonconserved Noether currents from the quantum effective action

Grossi E.
2022

Abstract

The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. Interestingly, the construction can be generalized beyond the standard symmetry transformations that leave the action invariant. We also discuss an extended set of transformations, which change the action by a term that is locally known on the level of the quantum effective action. Associated to such extended gauge transformations are currents for which we obtain a divergence-type equation of motion, but they are not conserved. We call them nonconserved Noether currents. We discuss, in particular, symmetries and extended transformations associated to space-time geometry for relativistic quantum field theories. These encompass local dilatations or Weyl gauge transformation, local Lorentz transformations, and local shear transformations. Together they constitute the symmetry group of the frame bundle GL(d). The corresponding nonconserved Noether currents are the dilatation or Weyl current, the spin current, and the shear current. In particular, for the latter, we obtain a new divergence-type equation of motion.
2022
105
0
1
Floerchinger S.; Grossi E.
File in questo prodotto:
File Dimensione Formato  
PhysRevD.105.085015.pdf

accesso aperto

Tipologia: Pdf editoriale (Version of record)
Licenza: Open Access
Dimensione 404.98 kB
Formato Adobe PDF
404.98 kB Adobe PDF

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1331173
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact