Abstract
In 1933 Dirac pointed out that it would be desirable to have a formulation of quantum mechanics in close correspondence to the Lagrangian method in classical mechanics, rather than to the more conventional Hamiltonian framework1). The Lagrangian method is based upon an action, defined as the time integral of the Lagrangian, and the principle of least action expresses the equations of motion in terms of a variational principle. The action is a relativistic invariant, and therefore the obvious advantage of this approach is that relativistic invariance is manifest at all stages. Feynman, in his pioneering work, fully developed this line of thought, and applied his methods to a large variety of problems 2,3). His work led to the notion of an integral over all paths, which is an integration in the space of functionals. Such integrations had actually been studied in the mathematical literature (for a review, see (4)).
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de Wit, B. (1982). Functional Methods in Quantum Field Theory. In: Lévy, M., Basdevant, JL., Speiser, D., Weyers, J., Jacob, M., Gastmans, R. (eds) Fundamental Interactions. NATO Advanced Study Institutes Series, vol 85. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3551-1_1
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