R. P. Feynman's paper "The Theory of Positrons" analyzes the behavior of positrons and electrons in external potentials, neglecting their mutual interaction. The solution to this problem is derived by reinterpreting the solutions of the Hamiltonian differential equations, which automatically includes all possibilities of virtual and real pair formation and annihilation, along with ordinary scattering processes. The "negative energy states" are represented as waves traveling backward in time from the external potential. Each electron is represented by a pair of positrons, one of which scatters the potential and annihilates the electron. The amplitude for a process involving multiple particles is the product of the transition amplitudes for each particle, and the exclusion principle is essential for consistent interpretation. The results are also expressed in momentum-energy variables, and the equivalence to the second quantization theory of holes is proven in an appendix. The paper introduces a Green's function treatment of the Schrödinger equation and extends it to the Dirac equation, providing a framework for understanding quantum electrodynamics.R. P. Feynman's paper "The Theory of Positrons" analyzes the behavior of positrons and electrons in external potentials, neglecting their mutual interaction. The solution to this problem is derived by reinterpreting the solutions of the Hamiltonian differential equations, which automatically includes all possibilities of virtual and real pair formation and annihilation, along with ordinary scattering processes. The "negative energy states" are represented as waves traveling backward in time from the external potential. Each electron is represented by a pair of positrons, one of which scatters the potential and annihilates the electron. The amplitude for a process involving multiple particles is the product of the transition amplitudes for each particle, and the exclusion principle is essential for consistent interpretation. The results are also expressed in momentum-energy variables, and the equivalence to the second quantization theory of holes is proven in an appendix. The paper introduces a Green's function treatment of the Schrödinger equation and extends it to the Dirac equation, providing a framework for understanding quantum electrodynamics.