On Hamiltonian Approach to Standard Model

TL;DR

This paper applies the Hamiltonian approach to the Standard Model, deriving a dynamic Higgs potential and predicting the Higgs mass, while highlighting the role of static interactions in off-mass-shell phenomena.

Contribution

It introduces a Hamiltonian formulation with a dynamic Higgs potential and predicts the Higgs mass using a new sum-rule, advancing the theoretical understanding of the Standard Model.

Findings

Predicts Higgs mass as 311.6 ± 8.9 GeV.

Highlights the importance of static interactions in off-mass-shell phenomena.

Provides a Hamiltonian framework for analyzing gauge models.

Abstract

The vector bosons models including Standard Model (SM) are investigated in the framework of the Dirac Hamiltonian method with explicit resolving the Gauss constraints in order to eliminate variables with zero momenta and negative energy contributions in accordance with the operator quantization principles. The Hamiltonian formulation admits the dynamic version of the Higgs potential, where its constant parameter is replaced by the dynamic zero Fourier harmonic of the very Higgs field. In this case, the zero mode equation is a new sum-rule that predicts mass of Higgs field $m_h=\sqrt{6m^2_t-4[2M_W^2+M_Z^2]}=311.6\pm 8.9 {\rm GeV}$. The Hamiltonian formulation leads to static interactions playing the crucial role in the off-mass-shell phenomena of the type of bound state and a kaon - pion transition in the weak nonleptonic decays.