Calculation in Peskin&Schroeder QFT book

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SUMMARY

The discussion focuses on resolving the calculation of equation (2.33) from the Peskin & Schroeder Quantum Field Theory (QFT) book. The user encounters difficulties after eliminating the divergent commutator, specifically with two extra terms: ap.a(-p) and a^+(-p).a^+p. The user identifies these terms as P(a_p a_{-p} - a^+_{-p} a^+_p), noting that both terms are odd functions due to the commutation of a_p and a_{-p}, leading to their integral equating to zero.

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT) principles
  • Familiarity with the Peskin & Schroeder textbook
  • Knowledge of commutation relations in quantum mechanics
  • Basic calculus, particularly integration of functions
NEXT STEPS
  • Review the derivation of equation (2.33) in Peskin & Schroeder
  • Study the properties of odd functions in quantum mechanics
  • Learn about divergent commutators and their elimination techniques
  • Explore advanced topics in Quantum Field Theory related to operator algebra
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Students and researchers in Quantum Field Theory, particularly those studying the Peskin & Schroeder textbook, as well as physicists dealing with operator algebra and commutation relations.

aleazk
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Hi, i can't get the result stated as equation (2.33) in page 22. To be more clear, after the elimination of the divergent commutator, i still have two extra terms that i don't know how to cancel out. the total extra term is ap.a(-p)-a^+(-p).a^+p. :confused:
 
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I think the extra terms are
[tex]{\bf{P}}({a_{\bf{p}}}{a_{ - {\bf{p}}}} - {a^ + }_{ - {\bf{p}}}{a^ + }_{\bf{p}})[/tex]
Notice that they are both odd function since a_p and a_(-p) are commute. Thus, the integration of them should be ZERO.
 

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