Abstract
We describe dual and antidual solutions of the Yang–Mills equations by means of L´evy Laplacians. To this end, we introduce a class of L´evy Laplacians parameterized by the choice of a curve in the group SO(4). Two approaches are used to define such Laplacians: (i) the Levy Laplacian can be defined as an integral functional defined by a curve in SO(4) and a special form of the second-order derivative, or (ii) the Levy Laplacian can be defined as the Cesaro mean of second-order derivatives along vectors from the orthonormal basis constructed by such a curve. We prove that under some conditions imposed on the curve generating the Levy Laplacian, a connection in the trivial vector bundle with base R4 is an instanton (or an anti-instanton) if and only if the parallel transport generated by the connection is harmonic for such a Levy Laplacian.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Steklov Institute of Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
