Pengming Zhang

Non-relativistic conformal symmetries in fluid mechanics

The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time. When the fluid is compressible, the symmetry is enlarged to the expanded Schrödinger group, which also involves, in addition, Schrödinger expansions. While incompressible fluid dynamics can be derived as an appropriate non-relativistic limit of a conformally invariant relativistic theory, the recently discussed conformal Galilei group, obtained by contraction from the relativistic conformal group, is not a symmetry. This is explained by the subtleties of the non-relativistic limit.

Sturm–Liouville and Carroll: at the heart of the memory effect

For a plane gravitational wave whose profile is given, in Brinkmann coordinates, by a

On microscopic structure of the QCD vacuum

2\times 2

Velocity Memory Effect for Polarized Gravitational Waves

2×2 symmetric traceless matrix K(U), the matrix Sturm–Liouville equation

Separability and Dynamical Symmetry of Quantum Dots

\ddot{P}=KP

Re-interpretation of Skyrme Theory: New Topological structures

P¨=KP plays a multiple and central rôle: (i) it determines the isometries; (ii) it appears as the key tool for switching from Brinkmann to BJR coordinates and vice versa; (iii) it determines the trajectories of particles initially at rest. All trajectories can be obtained from trivial “Carrollian” ones by a suitable action of the (broken) Carrollian isometry group.