Gravitational potential energy group theoretically
Joachim Nzotungicimpaye
TL;DR
This paper demonstrates that by symplectically realizing the Aristotle Lie group in one spatial dimension, the resulting elementary system's Hamiltonian comprises solely gravitational potential energy, with no kinetic component.
Contribution
It introduces a group-theoretic approach to derive a Hamiltonian containing only gravitational energy, expanding the understanding of symplectic realizations in physics.
Findings
Hamiltonian consists solely of gravitational energy
Symplectic realization of Aristotle Lie group in one spatial dimension
No kinetic term in the elementary system's Hamiltonian
Abstract
We show by symplectically realizing the one spatial Aristotle Lie group that the hamiltonian of the associated elementary system consist of a gravitational energy only. No kinetic term.
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Taxonomy
TopicsRelativity and Gravitational Theory