[Paper Review] Condensate mechanism of conformal symmetry breaking

V. N. Pervushin, A. B. Arbuzov+8 more|arXiv (Cornell University)|Nov 19, 2012

Cosmology and Gravitation Theories3 references3 citations

TL;DR

This paper proposes that conformal symmetry breaking in quantum field theories—such as QCD, the Minimal Standard Model, and Dirac conformal General Relativity—arises via normal ordering of field operators, leading to condensates and Casimir energies. This mechanism explains the Higgs boson mass without a Higgs potential, the low-energy Gell-Mann–Oakes–Renner relation, and supernova data in conformal cosmology without a cosmological constant.

ABSTRACT

The low energy Gell-Mann-Oakes-Renner relation, Higgs particle mass value, and the new observational cosmological data are considered as evidence of the condensate mechanism of conformal symmetry breaking at the quantum level. The condensate mechanism occurs by means of normal ordering of field operators in QCD, Minimal Standard Model of electroweak interactions without the Higgs potential, and the Dirac conformal General Relativity with long range forces.

Motivation & Objective

• To explain the origin of the Higgs boson mass in the Minimal Standard Model without invoking the Higgs potential.
• To demonstrate that the low-energy Gell-Mann–Oakes–Renner relation in QCD arises from quantum condensates due to normal ordering.
• To show that cosmological data, including supernova distances, can be explained in conformal gravity without a cosmological constant.
• To unify the mechanism of conformal symmetry breaking across QCD, electroweak theory, and gravity via vacuum condensates and Casimir energies.
• To establish a framework where the Planck epoch and electroweak scale emerge naturally from conformal invariance and vacuum energy.

Proposed method

• Applies the Dirac Hamiltonian scheme with a comoving frame defined by a time-like vector ℓμ to ensure Poincaré and gauge invariance in S-matrix elements.
• Uses normal ordering of field operators (e.g., gluons, quarks, Higgs) to generate effective masses and condensates, such as M_g^2 = 3g²(N_c²−1)C_gluon.
• Derives the Yukawa interaction in QCD from normal-ordered gluon condensates, leading to the Salpeter and Schwinger–Dyson equations.
• Applies the same condensate mechanism in the Dirac conformal General Relativity framework, where Casimir energy dominates in the void space approximation.
• Uses the Planck least action postulate to derive the scale factor at the Planck epoch, linking it to the Hubble constant and redshift.
• Classifies energy scales via Weyl group representations in tangent Minkowski space, assigning conformal weights to observed physical scales (e.g., CMB, electroweak, Planck).

Experimental results

Research questions

• RQ1 How can the Higgs boson mass emerge in the Minimal Standard Model without a Higgs potential?
• RQ2 What is the quantum origin of the Gell-Mann–Oakes–Renner relation in low-energy QCD?
• RQ3 Can supernova distance data be explained in a conformal cosmology without a cosmological constant?
• RQ4 How does normal ordering of field operators lead to effective masses and condensates in non-Abelian gauge theories?
• RQ5 What is the role of Casimir energy in the formation of primordial particles (e.g., Higgs, photons) in the early universe?

Key findings

• The Higgs boson mass in the Minimal Standard Model arises from normal ordering of the Higgs field, without requiring a Higgs potential.
• The Gell-Mann–Oakes–Renner relation in QCD is reproduced as a consequence of gluon condensate formation via normal ordering.
• The effective gluon mass M_g is derived as M_g² = 3g²(N_c²−1)C_gluon, with C_gluon being the gluon condensate.
• In conformal cosmology, the Hubble diagram of Type Ia supernovae is explained by the long space interval r_horizon(z) = H₀⁻¹(1+z)⁻², driven by Casimir energy.
• The Casimir energy in the Empty Universe Model accounts for the creation of ~10⁹⁰ Higgs bosons and ~10⁸⁷ photons with CMB temperature ~3 K.
• The Weyl group representations in tangent Minkowski space classify physical scales: n=3 gives M_EW ~ 10³ GeV, n=2 gives T_CMB ~ 10⁻¹² GeV, and n=1 gives nonrelativistic energy scale ~10⁻²⁷ GeV.