New Framework for Hamiltonian Dynamics Introduced

In a recent paper titled "Even More Generalized Hamiltonian Dynamics," authors W. A. Horowitz and A. Rothkopf present a new approach to deriving classical equations of motion within Hamiltonian phase space. This work focuses on particles subject to general position and velocity-dependent non-holonomic equality constraints. A significant aspect of their research is the introduction of Flannery brackets, which serve to generalize the well-known Poisson brackets.

The authors propose that these Flannery brackets could potentially replace Poisson brackets in Dirac's brackets, thereby offering a new quantization procedure for systems with non-holonomic equality constraints. The implications of this work could extend to various fields, including mathematical physics and high-energy physics, as it provides a framework for understanding complex dynamical systems under specific constraints.

The paper consists of three pages and includes one figure, outlining the foundational principles and conjectures related to the new brackets. This advancement could pave the way for further research into the quantization of constrained systems, enhancing our understanding of classical and quantum mechanics.

For those interested in the detailed findings, the paper can be accessed through arXiv at arXiv:2408.14420.