Form factors and equal-time commutators

• DOI: 10.1007/bf02729553
• Publication Date: 2007-12-18T08:37:10Z
• Authors: T. C. Yang
• Keywords: Commutator; Momentum (technical analysis); Momentum transfer; Fubini's theorem

We study the equal-time commutator of the charge and current sandwiched between states of unequal momenta, considering the momentum transfer between the two states as a new independent variable. One notes that usual current algebra sum rules are obtained at zero momentum transfer, probing the equal-time commutator by usingq2 (the 4-momentum square of the current) as a variable, namely, the Adler-Weisberger and the Cabibbo-Radicati sum rules. By our new approach, we study the dispersion method (Dashen-Fubini-Gell-Mann sum rule) and the current algebra method (using Ward identity, specifically the Weisberger approach). We find that they give the same result for the pion, but different results for the nucleon. The difference (due to spin) is traced down to the question of subtraction. We comment on that at the end.