arXiv subjects
Publications and source records attributed to Mickaya A. Razanaparany.
Within the framework of quantum theory, we review the Chrestenson operator, the Weyl operator basis, and the Kronecker-Pauli operator basis in $d$-dimensional Hilbert spaces using Dirac notation, where $d$ is a prime integer strictly greater than 2. We establish a new algebraic relation connecting these operators and present the cases $d=3$ and $d=5$ as illustrative examples.
Explicit analytic expressions for the electron self-energy and the vertex correction in quantum electrodynamics are derived at one loop using the recently proposed regularization scheme known as denominator regularization, assisted by its correspondence with dimensional regularization to determine the coefficient functions, which are a specific ingredient of this approach. We then show that the regularized amplitudes satisfy the Ward-Takahashi identity, thereby ensuring that gauge symmetry is preserved after regularization.