Looking for Carroll particles in two time spacetime
arXiv:2310.19050 · doi:10.1103/PhysRevD.109.025005
Abstract
We make an attempt to describe Carroll particles with a non-vanishing value of energy (i.e. the Carroll particles which always stay in rest) in the framework of two time physics, developed in the series of papers by I. Bars and his co-authors. In the spacetime with one additional time dimension and one additional space dimension one can localize the symmetry which exists between generalized coordinate and their conjugate momenta. Such a localization implies the introduction of the gauge fields, which in turn implies the appearance of some first-class constraints. Choosing different gauge-fixing conditions and solving the constraints one obtain different time parameters, Hamiltonians, and generally, physical systems in the standard one time spacetime. In this way such systems as non-relativistic particle, relativistic particles, hydrogen atoms and harmonic oscillators were described as dual systems in the framework of the two time physics. Here, we find a set of gauge fixing conditions which provides as with such a parametrization of the phase space variables in the two time world which gives the description of Carroll particle in the one time world. Besides, we construct the quantum theory of such a particle using an unexpected correspondence between our parametrization and that obtained by Bars for the hydrogen atom in 1999.
arXiv comment11 pages, 1 figure
References in corpus (33)
- Conformal Carroll groups and BMS symmetry
- Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
- Carrollian Physics at the Black Hole Horizon
- Carroll Structures, Null Geometry and Conformal Isometries
- Local Conformal Symmetry in Physics and Cosmology
- Conformal Carroll groups
- Dynamics of Carroll Particles
- Gauged Duality, Conformal Symmetry, and Spacetime with Two Times
- Carroll Expansion of General Relativity
- Antigravity and the big crunch/big bang transition
- S-Theory
- Theories with Two Times
- Supersymmetry, p-brane duality and hidden space and time dimensions
- Lifting M-theory to Two-Time Physics
- String and Particle with Two Times
- Magnetic Carrollian gravity from the Carroll algebra
- Conformal Symmetry and Duality between Free Particle, H-atom and Harmonic Oscillator
- Carroll/fracton particles and their correspondence
- Two-Time Physics in Field Theory
- Geodesically Complete Analytic Solutions for a Cyclic Universe
- Selection rules for the Wheeler-DeWitt equation in quantum cosmology
- Hidden Symmetries, AdS_D x S^n, and the lifting of one-time-physics to two-time-physics
- Complete Set of Homogeneous Isotropic Analytic Solutions in Scalar-Tensor Cosmology with Radiation and Curvature
- Gravity in 2T-Physics
- A case for 14 dimensions
- Geometry and Symmetry Structures in 2T Gravity
- The Big Bang and Inflation United by an Analytic Solution
- Lie algebraic Carroll/Galilei duality
- Time in quantum theory, the Wheeler-DeWitt equation and the Born-Oppenheimer approximation
- Dual Field Theories In (d-1)+1 Emergent Spacetimes From A Unifying Field Theory In d+2 Spacetime
- Black hole entropy reveals a 12th "dimension"
- Generalized Dualities in 1T-Physics as Holographic Predictions from 2T-Physics
- Duality Between Hydrogen Atom and Oscillator Systems via Hidden SO(d,2) Symmetry and 2T-physics