History of variational principles in physics involves integrals over an interval of time and (for fields) extended region of space. Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g., In particular, the fixing of the "final" state appears to give the action principle a teleological character which has been controversial historically. This apparent teleology is eliminated in the quantum mechanical version of the action principle. History of variational principles in physics A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an
Algebra of physical space equation, for an electrically charged particle of mass "m" and charge "e", takes the form: where e is an arbitrary unitary vector, and "A" is the electromagnetic paravector potential as above. The electromagnetic interaction has been included via minimal coupling in terms of the potential "A". The differential equation of the Lorentz rotor that is consistent with the Lorentz force is such that the proper velocity is calculated as the Lorentz transformation of the proper velocity at rest which can be integrated to find the space-time trajectory formula_31 with the additional use of Algebra of physical space In physics, the