التفاصيل البيبلوغرافية
| العنوان: |
Asymptotic freedom in the BV formalism. |
| المؤلفون: |
Elliott, Chris1 celliott@ihes.fr, Williams, Brian2 bwill@math.northwestern.edu, Yoo, Philsang3 philsang.yoo@yale.edu |
| المصدر: |
Journal of Geometry & Physics. Jan2018, Vol. 123, p246-283. 38p. |
| مصطلحات موضوعية: |
*ASYMPTOTIC freedom, *RENORMALIZATION (Physics), *QUANTUM perturbations, *MATHEMATICAL invariants, *YANG-Mills theory, *COHOMOLOGY theory |
| مستخلص: |
We define the β -function of a perturbative quantum field theory in the mathematical framework introduced by Costello – combining perturbative renormalization and the BV formalism – as the cohomology class of a certain functional measuring scale dependence of the effective interaction. We show that the one-loop β -function is a well-defined element of the obstruction–deformation complex for translation-invariant and classically scale-invariant theories, and furthermore that it is locally constant as a function on the space of classical interactions and computable as a rescaling anomaly, or as the logarithmic one-loop counterterm. We compute the one-loop β -function in first-order Yang–Mills theory, recovering the famous asymptotic freedom for Yang–Mills in a mathematical context. [ABSTRACT FROM AUTHOR] |
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