ABSTRACT
To formulate the Dirac theory, one first of all must start with definitions of positive and negative states of the electron. If the operator of electron kinetic energy is denoted as T and the operator of its modulus as |T |, the operator of the kinetic energy sign is
ε = T
|T | . (1)
The eigenfunction ψ+ of the operator ε, corresponding to the eigenvalue ε = +1, describes the “positive” state, while the eigenfunction ψ−, corresponding to the eigenvalue ε = −1, describes the “negative” state of an electron. An arbitrary wave function ψ might be represented as a sum ψ = ψ+ + ψ−. The set of matrix elements of an operator corresponding to transitions from ψ+ to ψ− represents, according to Schro¨dinger, the odd part of the operator considered, while all the other matrix elements represent its even part.
