Numerical Mathematica Notebooks for Electroweak Theory with Gamma Matrices and Fermion–Boson Duality

This dataset contains Wolfram Mathematica notebooks and PDF exports used to perform numerical checks and visualizations for a theoretical study of the electroweak sector based on symmetry broken gamma matrices and fermion boson duality.

The materials include a notebook that derives and evaluates the electroweak gauge boson mass terms using a four dimensional gamma matrix embedding of the SU(2) left times U(1) hypercharge gauge structure. In this notebook, Dirac gamma matrices are defined and their algebra is verified, the weak generators and hypercharge operator are embedded into a four component lepton and Higgs space, the Higgs covariant derivative is constructed, and the mass terms of the charged and neutral gauge bosons are extracted and numerically evaluated for representative parameter values.

A second notebook constructs and analyzes bosonic gamma matrices built from two equivalent Dirac systems. It verifies their modified algebra, shows explicitly that only the transverse degrees of freedom survive, and illustrates how unphysical time like and longitudinal components are projected out. This is directly related to gauge symmetry, chiral structure, the Ward Takahashi identity, and BRST symmetry.

A third notebook visualizes an energy dependent transition function used in the fermion boson duality framework. It plots the effective fermionic and bosonic components as functions of energy, provides an interactive interface to scan over energy, and includes example code to export simple animations.

Together, these files document the numerical backbone of the analysis, in particular the consistency of the gamma matrix based formulation with standard electroweak mass generation, and the behavior of the bosonic gamma matrices and the duality inspired transition function. The notebooks can be adapted by changing input parameters such as couplings, vacuum expectation value, and transition scale, and are intended to make all algebraic steps and numerical checks transparent and reproducible.