Boundary dynamics of Maxwell-invariant three-dimensional Chern-Simons gravity
Journal of High Energy PhysicsWe construct a two-dimensional dual field theory induced at the boundary of three-dimensional Chern-Simons gravity invariant under the Maxwell algebra. The resulting action takes the form of a Maxwellian extension of the flat Liouville theory known from ...
Felix Höfenstock +1 more
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Phase-locking in dynamical systems and quantum mechanics
Journal of High Energy PhysicsIn this study, we discuss the Prüfer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schrödinger equation with periodic potential.
Artem Alexandrov +2 more
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Coset symmetries and coadjoint orbits
Proceedings of Modave Summer School in Mathematical Physics — PoS(Modave2024)In these lectures we review two approaches to constructing particle actions from coset spaces of symmetry groups: non-linear realisations and coadjoint orbits. At the level of particle actions, we observe that they coincide. We also provide an introduction to symplectic geometry and we sketch the theory of coadjoint orbits for the Poincaré group.
Lahlali, Ismaël Ahlouche +1 more
openaire +2 more sources
Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation. [PDF]
Entropy (Basel), 2020 Barbaresco F.
europepmc +1 more source
A Structural Approach to Relativistic Symmetry: Dual Relativity and the Lorentz–Heisenberg Algebra
MathematicsThis paper studies a realization-theoretic problem inside the standard Lorentz-covariant Fourier-dual framework on L2(R3,1): whether position-space and momentum-space geometric translations can be placed on equal structural footing without leaving the ...
Daniel Rothbaum
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From the Jordan Product to Riemannian Geometries on Classical and Quantum States. [PDF]
Entropy (Basel), 2020 Ciaglia FM, Jost J, Schwachhöfer L.
europepmc +1 more source
Joseph Fourier 250th Birthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century. [PDF]
Entropy (Basel), 2019 Barbaresco F, Gazeau JP.
europepmc +1 more source
Higher Order Geometric Theory of Information and Heat Based on Poly-Symplectic Geometry of Souriau Lie Groups Thermodynamics and Their Contextures: The Bedrock for Lie Group Machine Learning. [PDF]
Entropy (Basel), 2018 Barbaresco F.
europepmc +1 more source
Normal forms for Poisson maps and symplectic groupoids around Poisson transversals. [PDF]
Lett Math Phys, 2018 Frejlich P, Mărcuț I.
europepmc +1 more source