Lorentz and Galilei Invariance on Lattices
arXiv:hep-th/0310013 · doi:10.1103/PhysRevD.69.105011
Abstract
We show that the algebraic aspects of Lie symmetries and generalized symmetries in nonrelativistic and relativistic quantum mechanics can be preserved in linear lattice theories. The mathematical tool for symmetry preserving discretizations on regular lattices is the umbral calculus.
5 pages
References in corpus (18)
- Lorentz-Violating Extension of the Standard Model
- Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
- Discreteness of area and volume in quantum gravity
- Nonstandard optics from quantum spacetime
- Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
- Modern Michelson-Morley experiment using cryogenic optical resonators
- Lectures on Loop Quantum Gravity
- Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
- Dynamical Initial Conditions in Quantum Cosmology
- Quantum-Gravity Phenomenology: Status and Prospects
- Canonical quantization of general relativity in discrete space-times
- Lie-algebraic discretization of differential equations
- Consistency Conditions for Fundamentally Discrete Theories
- Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign
- Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice
- Discrete quantum gravity: applications to cosmology
- Discrete derivatives and symmetries of difference equations
- Combinatorial dynamics in quantum gravity
Cited by in corpus (9)
- Continuous Symmetries of Difference Equations
- Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation
- Discretization of partial differential equations preserving their physical symmetries
- Heisenberg Algebra, Umbral Calculus and Orthogonal Polynomials
- Discrete Differential Geometry on causal graphs
- Integrable maps from Galois differential algebras, Borel transforms and number sequences
- Umbral Deformations on Discrete Spacetime
- Conformally invariant elliptic Liouville equation and its symmetry preserving discretization
- Umbral Vade Mecum