Christian Duval

Conformal Carroll groups

Conformal extensions of Levy–Leblondʼs Carroll group, based on geometric properties analogous to those of Newton–Cartan space-time are proposed. The extensions are labeled by an integer k. This framework includes and extends our recent study of the Bondi–Metzner–Sachs (BMS) and Newman–Unti (NU) groups. The relation to conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by ‘Carrollian photons’. Motion both in the Newton–Cartan and Carroll spaces may be related to that of strings in the Bargmann space.

Conformal symmetry of the coupled Chern-Simons and gauged nonlinear Schrödinger equations

Abstract The non-relativistic conformal symmetry found by Jackiw and Pi for the coupled Chern-Simons and gauged nonlinear Schrodinger equations in the plane is derived in a non-relativistic Kaluza-Klein framework.

Spinors in Non-relativistic Chern–Simons Electrodynamics

Abstract It is shown that the non-relativistic “Dirac” equation of Levy-Leblond, we used recently to describe a spin 1 2 field interacting non-relativistically with a Chern–Simons gauge field, can be obtained by lightlike reduction from 3+1 dimensions. This allows us to prove that the system is Schrodinger symmetric. A spinor representation of the Schrodinger group is presented. Static, self-dual solutions, describing spinor vortices are given and shown to be the non-relativistic limits of the fermionic vortices found by Choet al. The construction is extended to external harmonic and uniform magnetic fields.

Comment on "berry phase correction to electron density of states in solids"

A Comment on the Letter by Di Xiao, Junren Shi, and Qian Niu, Phys. Rev. Lett. 95, 137204 (2005). The authors of the Letter offer a Reply.

Spinors in non-relativistic Chern{endash}Simons electrodynamics

Abstract It is shown that the non-relativistic “Dirac” equation of Levy-Leblond, we used recently to describe a spin 1 2 field interacting non-relativistically with a Chern–Simons gauge field, can be obtained by lightlike reduction from 3+1 dimensions. This allows us to prove that the system is Schrodinger symmetric. A spinor representation of the Schrodinger group is presented. Static, self-dual solutions, describing spinor vortices are given and shown to be the non-relativistic limits of the fermionic vortices found by Choet al. The construction is extended to external harmonic and uniform magnetic fields.

Vanishing of the conformal anomaly for strings in a gravitational wave

Abstract Using the non-symmetric-connection approach proposed by Osborn, we demonstrate that, for a bosonic string in a specially chosen plane-fronted gravitational wave and an axion background, the conformal anomaly vanishes at the two-loop level. Under some conditions, the anomaly vanishes at all orders.

Soft gravitons and the memory effect for plane gravitational waves

The “gravitational memory effect” due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with the analogue of “soft gravitons for this nonasymptotically flat system. We explain how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constructed. It is also shown how to extend our treatment to Einstein-Maxwell plane waves and a midisuperspace quantization is given.

On the projective geometry of the supercircle: a unified construction of the super cross-ratio and Schwarzian derivative

We consider the standard contact structure on the supercircle, S^{1|1}, and the supergroups E(1|1), Aff(1|1) and SpO(2|1) of contactomorphisms, defining the Euclidean, affine and projective geometry respectively. Using the new notion of (p|q)-transitivity, we construct in synthetic fashion even and odd invariants characterizing each geometry, and obtain an even and an odd super cross-ratios. Starting from the even invariants, we derive, using a superized Cartan formula, one-cocycles of the group of contactomorphisms, K(1), with values in tensor densities F_\lambda(S^{1|1}). The even cross-ratio yields a K(1) one-cocycle with values in quadratic differentials, Q(S^{1|1}), whose projection on F_{3/2}(S^{1|1}) corresponds to the super Schwarzian derivative arising in superconformal field theory. This leads to the classification of the cohomology spaces H^1(K(1),F_\lambda(S^{1|1})). The construction is extended to the case of S^{1|N}. All previous invariants admit a prolongation for N>1, as well as the associated Euclidean and affine cocycles. The super Schwarzian derivative is obtained from the even cross-ratio, for N=2, as a projection to F_1(S^{1|2}) of a K(2) one-cocycle with values in Q(S^{1|2}). The obstruction to obtain, for N\geq 3, a projective cocycle is pointed out.

Wigner–Souriau translations and Lorentz symmetry of chiral fermions

Abstract Chiral fermions can be embedded into Souriaus massless spinning particle model by “enslaving” the spin, viewed as a gauge constraint. The latter is not invariant under Lorentz boosts; spin enslavement can be restored, however, by a Wigner–Souriau (WS) translation, analogous to a compensating gauge transformation. The combined transformation is precisely the recently uncovered twisted boost, which we now extend to finite transformations. WS-translations are identified with the stability group of a motion acting on the right on the Poincare group, whereas the natural Poincare action corresponds to action on the left.

Eisenhart lifts and symmetries of time-dependent systems

Certain dissipative systems, such as Caldirola and Kannais damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with