Implications of conformal invariance in momentum space

Conformal invariance in hydrodynamic turbulence

This short survey is written by a physicist. It contains neither theorems nor precise definitions. Its main content is a description of the results of numerical solution of the equations of fluid mechanics in the regime of developed turbulence. Due to limitations of computers, the results are not very precise. Despite being neither exact nor rigorous, the findings may nevertheless be of interes...

Conformal invariance from non-conformal gravity

We discuss the conditions under which classically conformally invariant models in four dimensions can arise out of non-conformal (Einstein) gravity. As an ‘existence proof’ that this is indeed possible we show how to derive N = 4 super Yang Mills theory with any compact gauge group G from non-conformal gauged N = 4 supergravity as a special flat space limit. We stress the role that the anticipa...

Noether symmetries, energy-momentum tensors and conformal invariance in classical field theory

In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on board, we next discuss in detail, for Poincaré invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a fam...

Chapter 18 Conformal Invariance

At the beginning of the semester we motivated our investigation of symmetries by illustrating that, given differential equations which were symmetric, the solutions had to transform into each other under the symmetries as a representation of the symmetry. The first illustrations considered Schrödinger equations with symmetric potentials, such as the electrons in the spherically symmetric potent...

Conformal invariance of domino tiling