 Although these developments were only indirectly influenced by Dirac, by way of the mathematical developments that are associated with his formal approach to quantum mechanics, there are other elements of his work that had a more direct and very substantial impact on the development of QFT. In the 1930s, Dirac (1933) developed a Lagrangian formulation of quantum mechanics and applied it to quantum fields , and the latter inspired Feynman (1948) to develop the path-integral approach to QFT. The mathematical foundation for path-integral functionals is still lacking (Rivers 1987, pp, 109–134), though substantial progress has been made (DeWitt-Morette et al. 1979). Despite such shortcomings, it remains the most useful and influential approach to QFT to date. In the 1940s, Dirac (1943) developed a form of quantum electrodynamics that involved an indefinite metric – see also Pauli (1943) in that connection. This had a substantial influence on later developments, first in quantum electrodynamics in the early 1950s with the Gupta-Bluer formalism, and in a variety of QFT models such as vector meson fields and quantum gravity fields by the late 1950s – see Chapter 2 of Nagy (1966) for examples and references.