What is Schwinger terms and what is the origin?

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SUMMARY

The discussion centers on Schwinger terms, specifically their relationship with the commutator of currents in quantum field theory. Schwinger terms arise as the gradient of the delta function in the commutator of the time component J^0(x) and the spatial component J^i(y) of the current. The conversation also addresses the appearance of infinities when considering products of operators at the same spacetime point, particularly in loop diagrams, questioning the origin of these infinities in the context of commutators.

PREREQUISITES
  • Quantum field theory fundamentals
  • Understanding of commutators in quantum mechanics
  • Knowledge of current operators J^0 and J^i
  • Familiarity with loop diagrams and their implications
NEXT STEPS
  • Study the derivation of Schwinger terms in quantum field theory
  • Explore the role of delta functions in commutation relations
  • Investigate regularization techniques for handling infinities in loop diagrams
  • Learn about the implications of operator products at the same spacetime point
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The discussion is beneficial for theoretical physicists, quantum field theorists, and advanced students seeking to deepen their understanding of commutation relations and the nature of infinities in quantum mechanics.

ndung200790
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What is Schwinger terms that related with commutator of currents and what is the origin?Why the infinities appear when we consider the product of operators of fields at the same spacetime point?
 
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The Schwinger term is the gradien of delta function term in commutator of J^0(x) and J^i(y).Then my question is:The infinities appear when we consider loop diagrams,but why the infinities(gradien of delta function) appear in the commutator?Where is the loops?
 

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