Contact symmetries of constrained systems and the associated integrals of motion

4th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Dimakis, N.^1 ; Terzis, Petros A.^2 ; Christodoulakis, T.^2

Instituto de Ciencias Fisicas y Matematicas, Universidad Austral de Chile, Valdivia, Chile^1

Nuclear and Particle Physics Section, Physics Department, University of Athens, Athens

GR 157-71, Greece^2

关键词: Conformal factors;    Constrained systems;    Degree of freedom;    Gauge conditions;    Infinitesimal generator;    Integrals of motion;    Loss of symmetry;    Relativistic particles;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/633/1/012040/pdf
DOI  :  10.1088/1742-6596/633/1/012040

来源: IOP

【 摘 要 】

The conditions for the existence of (polynomial in the velocities) contact symmetries of constrained systems that are described by quadratic Lagrangians is presented. These Lagrangians mainly appear in mini-superspace reductions of gravitational plus matter actions. In the literature, one usually adopts a gauge condition (mostly for the lapse N) prior to searching for symmetries. This, however, is an unnecessary restriction which may lead to a loss of symmetries and consequently to the respective integrals of motion. A generalization of the usual procedure rests in the identification of the lapse function N as an equivalent degree of freedom and the according extension of the infinitesimal generator. As a result, conformal Killing tensors (with appropriate conformal factors) can define integrals of motion (instead of just Killing tensors used in the regular gauge fixed case). An example of a relativistic particle in a pp-wave space-time and under the influence of a quadratic potential is illustrated.