Planar Carrollian statistical physics is well-defined thanks to central extensions and rotation, yielding logarithmic entropy scaling with disc area and two-dimensional ideal-gas pressure.
Planar Carrollean dynamics, and the Carroll quantum Hall effect
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abstract
We expand on the known result that the Carroll algebra in $2+1$ dimensions admits two non-trivial central extensions by computing the associated Lie group, which we call extended Carroll group. The symplectic geometry associated to this group is then computed to describe the motion of planar Carroll elementary particles, in the free case, when coupled to an electromagnetic field, and to a gravitational field. We compare to the motions of Carroll particles in $3+1$ dimensions in the same conditions, and also give the dynamics of Carroll particles with spin. In an electromagnetic background, the planar Carroll dynamics differ from the known Carroll ones due to 2 new Casimir invariants, and turn out to be non-trivial. The coupling to a gravitational field leaves the dynamics trivial, however. Finally, we obtain the quantum equation obeyed by Carroll wave functions \textit{via} geometric quantization.
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The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
New BMS3-invariant 2D scalar theories (electric, magnetic, canonical, coupled) with boundary analysis, flux laws, monodromy matching to 3D gravity, and complementary AdS3/dS3 flat limits.
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Statistical Physics of Planar Carroll Systems
Planar Carrollian statistical physics is well-defined thanks to central extensions and rotation, yielding logarithmic entropy scaling with disc area and two-dimensional ideal-gas pressure.
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The Free Particle--Oscillator--Inverted Oscillator Triangle: Conformal Bridges, Metaplectic Rotations and $\mathfrak{osp}(1|2)$ Structure
The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
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BMS$_3$ invariant field theories
New BMS3-invariant 2D scalar theories (electric, magnetic, canonical, coupled) with boundary analysis, flux laws, monodromy matching to 3D gravity, and complementary AdS3/dS3 flat limits.