[Paper Review] Quantum Field Theory and the Internal States of Elementary Particles

J.M. Greben|arXiv (Cornell University)|Jul 22, 2012

Particle physics theoretical and experimental studies7 references3 citations

TL;DR

This paper proposes a non-perturbative quantum field theory framework that derives massive, finite-sized quarks from massless bare quarks and gluons via self-consistent, coupled field equations in QCD with a zero Higgs field. It shows that non-linear dynamics and general relativity stabilize the system at 8.8 Planck lengths, yielding a 3.2 MeV mass in agreement with experiment, suggesting a fundamental origin for quark masses and the three generations via solutions to Higgs field equations.

ABSTRACT

A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent fields satisfying coupled quantum field equations, all expressed at the same space-time coordinate. Quantization is realized by expanding the quantum fields in terms of fermionic creation and annihilation operators. This approach is applied in a QCD description of the light quarks with a zero Higgs field. Originally massless and pointlike, an isolated quark (described in its own center-of-mass) acquires mass and a finite extent when treated as an interacting system of quark and gluon fields. The binding mechanism of this localized system has a topological character, being a consequence of the non-linear nature of QCD, while being insensitive to the magnitude of the coupling constant to lowest order. To prevent this system from collapsing general relativity is introduced. The quark stabilizes at a radius of 8.8 Planck lengths and acquires a mass of 3.2 MeV, in remarkable agreement with accepted phenomenological values. It is suggested that the two higher generations of quarks are associated with the other two real solutions of the Higgs field equations.

Motivation & Objective

• To develop a non-perturbative quantum field theory approach that describes the internal dynamics and mass generation of elementary particles from more fundamental, bare degrees of freedom.
• To explain the origin of quark masses without relying on the Higgs mechanism, using only QCD and general relativity.
• To explore whether the three generations of quarks emerge from multiple real solutions of the Higgs field equations in a fundamental theory.
• To unify the description of dressed fermions by treating fermionic and bosonic fields as interdependent, satisfying coupled field equations at the same spacetime point.
• To demonstrate that the mass and size of a quark arise from self-consistent, non-linear dynamics and gravitational stabilization, rather than from explicit mass terms.

Proposed method

• Treats fermionic and bosonic quantum fields as interdependent fields satisfying coupled quantum field equations at the same spacetime coordinate, without perturbative expansion.
• Uses operator expansions in terms of fermionic creation and annihilation operators to quantize the fields, enabling exact solutions at the operator level.
• Applies the R-product formalism to handle non-commutative operator products, preserving algebraic simplicity in the field equations.
• Introduces a vacuum projection operator Σ∞ that acts as a one-body projector, ensuring the state vector remains simple despite many-body components in the field operators.
• Imposes general relativity to prevent gravitational collapse, stabilizing the quark at a finite radius.
• Solves the coupled field equations exactly using generalized operator factorials and projection techniques, avoiding perturbative approximations.

Experimental results

Research questions

• RQ1 Can quark masses and finite size emerge dynamically from QCD alone, without explicit mass terms or the Higgs mechanism?
• RQ2 How does the non-linear structure of QCD generate a stable, self-bound quark state with finite extent and mass?
• RQ3 What role does general relativity play in stabilizing a self-consistent, interacting quark-gluon system against gravitational collapse?
• RQ4 Can the three generations of quarks arise from multiple real solutions of the Higgs field equations in a fundamental theory with φ=0?
• RQ5 Why do the effective masses of light quarks (e.g., 3.2 MeV) match phenomenological values if the fundamental theory contains only massless, pointlike quarks?

Key findings

• The quark stabilizes at a radius of 8.8 Planck lengths due to the interplay of QCD's non-linear dynamics and general relativity.
• The resulting quark mass is 3.2 MeV, in excellent agreement with the accepted phenomenological value for the light quark sector.
• The mass and size emerge from self-consistent solutions of coupled fermionic and gluonic field equations, without explicit mass terms or Higgs coupling.
• The exact solution of the operator field equations yields a dressed quark state described by a single creation operator, despite the presence of many-body components in the field operators.
• The system's stability is insensitive to the coupling constant at lowest order, indicating a topological binding mechanism rooted in QCD's non-linearity.
• The three generations of quarks may originate from three real solutions of the Higgs field equations, with the zero-Higgs case corresponding to the first generation.