The Dirac Equation: Unifying Quantum Mechanics and Relativity

Ijaz Durrani

Nyla T. Husain

Wei Wen

The Feynman path integral plays a central role in quantum mechanics, linking classical action to propagators and relating quantum electrodynamics (QED) to Feynman diagrams. However, the path-integral formulations used in non-relativistic quantum mechanics and in QED are neither unified nor directly connected. This suggests the existence of a missing path integral that bridges relativistic action and the Dirac equation at the single-particle level. In this work, we analyze the consistency and completeness of existing path-integral theories and identify a spinor path integral that fills this gap. Starting from a relativistic action written in spinor form, we construct a spacetime path integral whose kernel reproduces the Dirac Hamiltonian. The resulting formulation provides a direct link between the relativistic classical action and the Dirac equation, and it naturally extends the scalar relativistic path integral developed in our earlier work. Beyond establishing this structural connection, the spinor path integral offers a new way to interpret the origin of classical mechanics for the Dirac equation and suggests a spacetime mechanism for spin and quantum nonlocal correlations. These features indicate that the spinor path integral can serve as a unifying framework for existing path-integral approaches and as a starting point for further investigations into the spacetime structure of quantum mechanics.

Fu Yuhua

One of the reasons for 1933 Nobel Prize for physics is “for the discovery of new productive forms of atomic theory” (namely Schrodinger equation and Dirac equation). While, this paper points out that Schrodinger equation and Dirac equation are improper. According to Neutrosophy, Schrodinger equation and Dirac equation have three situations of truth, falsehood and indeterminacy respectively. Three reasons lead to Schrodinger equation and Dirac equation are improper: firstly, they are not derived by the principle of conservation of energy; secondly, the random (stochastic) concept could lead to absurd results; thirdly, they cannot solve many problems such as gravitation. Applying partial and temporary unified theory of natural science so including all the equations of natural science so far (in which, the theory of everything to express all of natural laws, described by Hawking that a single equation could be written on a T-shirt, is partially and temporarily realized in the form of partial and temporary unified variational principle of natural science so far), this paper presents partial and temporary unified theory of quantum mechanics so far, this unified theory can be used to make Schrodinger equation and Dirac equation tend to be proper (making Schrodinger equation and Dirac equation are restricted (or constrained) by principle of conservation of energy, and thus they can satisfy the principle of conservation of energy; also making they are restricted (or constrained) by a certain gravitational theory, and establish partial and temporary unified theory of quantum-gravitation so far).