# Dr Mahmut Elbistan

LE STUDIUM Research Guest Fellow

### From

Institute of Modern Physics (IMP), CAS - CN

### In residence at

Institut Denis Poisson (IDP) / CNRS, University of Orléans, University of Tours - FR

### Host scientist

Prof. Peter Horvathy

## PROJECT

**Chiral Particles, Anomalies, and Helicity**

Chiral particles have attracted considerable recent interest, both in particle and in condensed physics. Our particular interest lies in their anomalous transport properties and their helicity non-conservation in the presence of interactions.

Quantum field theory anomalies can be realized as emergent phenomena in condensed matter physics. For instance, the chiral anomaly occurs also in Weyl semimetals. Moreover, it yields the anomalous transport properties like the chiral magnetic effect and the anomalous Hall effect. More recently, new anomaly–induced transport phenomena, based on the conformal anomaly called "the scale magnetic effect" and "the scale electric effect" were found. We will work out whether there exists a realization also for the scale electric effect in Dirac/Weyl semimetals.

Secondly, we will consider duality symmetry and its conserved charge called the "optical helicity" in condensed matter systems. Classically, this charge can be written as a combination of two Chern-Simons terms. After quantization it corresponds to the difference of total numbers of right and left circularly polarized photons. We will investigate the consequences of the non-conservation of the optical helicity in topological magnetoelectric systems. In particular, the evolution of the quantized optical helicity might be very useful for a better understanding of Weyl semimetals and topological insulators.

## Publications

The integrals of the motion associated with conformal Killing vectors of a curved space–time with an additional electromagnetic background are studied for massive particles. They involve a new term which might be non-local. The difficulty disappears for pp-waves, for which explicit, local conserved charges are found. Alternatively, the mass can be taken into account by “distorting” the conformal Killing vectors. The relation of these non-point symmetries to the charges is analysed both in the Lagrangian and Hamiltonian approaches, as well as in the framework of Eisenhart–Duval lift.

The recently discovered conserved quantity associated with Kepler rescaling is generalized by an extension of Noether’s theorem which involves the classical action integral as an additional term. For a free particle, the familiar Schrödinger dilations are recovered. A general pattern arises for homogeneous potentials. The associated conserved quantity allows us to derive the virial theorem. The relation to the Bargmann framework is explained and illustrated by exact plane gravitational waves.