Classical Mass Generation in a Lattice U(1) Model with Higgs Mechanism: Analytical and Numerical Control
Year: 2026
Type: article
Abstract: This note presents a controlled classical analysis of a lattice U (1) model with a Higgsfield on a three-dimensional cubic lattice. We verify numerically that the vacuum expec-tation value ρ20 = −a/b and the gauge-field mass m2A = κρ20 are reproduced with machineprecision. It is shown that the energy of a pair of static charges is exactly expressedthrough the lattice Green function without any fitting parameters:Epair(r) = βQ2 G(0; m2A) − G(r; m2A) .The defect mass factorizes as mdef = βQ2F (m2A), where F is a monotonically decreasingfunction of m2A, in agreement with the analytic formula. The dependence of the latticecorrelation mass mlat on the bare mass mA is also checked; the obtained values approachthe theoretical curve 2 arsinh(mA/2). This provides a self-contained classical foundationfor future quantization.
Author: Gromov, Alexey
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204184241