TL;DR
This paper explores SL(2,R) invariant Hamiltonian systems using the orbit method, highlighting their global phase space structure, the role of time variable choices, and the implications for 1+0-dimensional space-time.
Contribution
It provides a detailed analysis of conformal mechanics within the orbit method framework, emphasizing global properties and the operational definition of time.
Findings
Dynamics and symmetries are globally well-defined on phase space.
Flexibility in time variable choice relates to the global structure of 1+0-dimensional space-time.
Discusses the operational definition of time in conformal mechanics.
Abstract
The SL(2,R) invariant Hamiltonian systems are discussed within the frame- work of the orbit method. It is shown that both dynamics and symmetry trans- formations are globally well-defined on phase space. The flexibility in the choice of time variable and Hamiltonian function described in the paper by de Alfaro et al. (Nuovo Cim. 34A (1976),569) is related to the nontrivial global structure of 1 + 0-dimensional space-time. The operational definition of time is discussed.
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