While many fundamental branches of physics, such as Newtonian mechanics, thermodynamics and special relativity, are founded on physical principles or laws, the basic assumptions for others, such as Hamiltonian, Lagrangian and quantum mechanics, lie in their respective mathematical frameworks. In this work, we aim to rederive and reorganize such topics identifying suitable physical assumptions that lead necessarily to the known results. Such endeavor and the consequent insights strive to be physically meaningful, philosophically consistent and mathematically precise.
Presented at the 33rd Summer Conference on Topology and its Applications, Western Kentucky University, July, 2018
Published in the Journal of Physics Communications, 2018
Presentation at the 18th UK and European Conference on Foundations of Physics, London School of Economics, July, 2016