Gents: Combining Chiral Currents with Translational Invariance

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SUMMARY

The discussion centers on the compatibility of non-singular chiral currents with translational invariance in quantum field theory. The primary concern is the use of point-splitting regularization, which effectively removes singularities from chiral currents but simultaneously disrupts translational invariance. Participants explore the implications of this trade-off and question the validity of the initial inquiry regarding the coexistence of these two properties.

PREREQUISITES
  • Understanding of chiral currents in quantum field theory
  • Familiarity with translational invariance principles
  • Knowledge of point-splitting regularization techniques
  • Basic concepts of fermionic operators and their properties
NEXT STEPS
  • Research advanced techniques in quantum field theory regularization methods
  • Explore the implications of breaking translational invariance in physical theories
  • Study the mathematical formulation of chiral anomalies
  • Investigate alternative regularization methods that preserve translational invariance
USEFUL FOR

The discussion is beneficial for theoretical physicists, quantum field theorists, and researchers focusing on chiral anomalies and regularization techniques in particle physics.

Neitrino
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Gents,

Is it possible to have the not singular chiral current (singularity is due to the product of fermionic operators) and at the same time the translational invariance. Normaly to get rid of singularity in chiral current one is useing the point splitting regularisation (little shift of arguments of fermionic fields on epsilon) which spoils the translational invariance.

Thank you
 
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