Legendre transformations and Clairaut-type equations

Abstract

It is noted that the Legendre transformations in the standard formulation of quantum field theory have the form of functional Clairaut-type equations. It is shown that in presence of composite fields the Clairaut-type form holds after loop corrections are taken into account. A new solution to the functional Clairaut-type equation appearing in field theories with composite fields is found.

13 pages

References in corpus (3)

• Exact evolution equation for the effective potential
• Loop expansion of the average effective action in the functional renormalization group approach
• Cho-Duan-Ge decomposition of QCD in the constraintless Clairaut-type formalism

Cited by in corpus (5)

• K-nonizing
• Gauge gravity vacuum in constraintless Clairaut-type formalism
• Non-Abelian gauge theories with composite fields in the background field method
• Gauge dependence of alternative flow equation for the functional renormalization group
• Basic properties of an alternative flow equation in gravity theories