Generation of new symmetries from explicit symmetry breaking

Abstract

We study how the explicit symmetry breaking, through a continuous parameter in the Lagrangian, can actually lead to the creation of different types of symmetries. As examples we consider the motion of a relativistic particle in a curved background, where a nonzero mass breaks the symmetry of the conformal algebra of the metric, and the motion in a Bogoslovsky-Finsler space-time, where a Lorentz violation takes place. In the first case, new nonlocal conserved charges emerge in the place of those which were previously generated by the conformal Killing vectors, while in the second, rational in the momenta integrals of motion appear to substitute the linear expressions corresponding to those boosts which fail to be symmetries.

arXiv comment10 pages, no figures, Latex2e source file, talk presented in the IC-MSQUARE 2021 conference

References in corpus (14)

• Invariant Variation Problems
• The Relation between Physical and Gravitational Geometry
• General Very Special Relativity is Finsler Geometry
• Classical kinematics for Lorentz violation
• Lie and Noether symmetries of geodesic equations and collineations
• Lie - point and variational symmetries in minisuperspace Einstein's gravity
• Finsler-like structures from Lorentz-breaking classical particles
• Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model Extension
• Classical Lagrangians for Momentum Dependent Lorentz Violation
• A generalized Noether theorem for scaling symmetry
• Conformal symmetries and integrals of the motion in pp waves with external electromagnetic fields
• Very Special Relativity and Lorentz Violating Theories
• Axion Mass Bound in Very Special Relativity
• Exact black hole solutions in Einstein-Aether Scalar field theory