Abstract
FEYNMAN1 has given a path integral formulation of non-relativistic quantum theory which he showed to be completely equivalent to that given by Schrödinger's equation. Although the same can be done for the existing relativistic theory2, it cannot be unique because the latter is not consistent. The fundamental dilemma is3: either one adopts unitarity and all the divergences that go with it, or else admits non-Hermitian interactions and thus the non-conservation of probability.
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References
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GOODALL, M. Path Integral Formulation of Relativistic Quantum Mechanics. Nature 196, 370 (1962). https://doi.org/10.1038/196370a0
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DOI: https://doi.org/10.1038/196370a0
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