[Paper Review] Confinement and U(1,3) symmetry of color particles in a complex phase space

V. V. Khruschev|ArXiv.org|Nov 26, 2003

Quantum Chromodynamics and Particle Interactions1 references3 citations

TL;DR

This paper proposes that U(1,3) symmetry in a complex phase space naturally generates a confining potential for quarks and gluons, with parameters derived from hadron spectroscopy and lattice QCD. The resulting scalar potential grows linearly at large distances, yielding a string tension σ ≈ 0.20 GeV² and a confinement mass m_c ≈ 0.45 GeV, consistent with nonperturbative QCD phenomena including the L"uscher term.

ABSTRACT

It is shown that a universal confining potential for hadron constituents can be obtained with the help of U(1,3) symmetry in a complex phase space. Parameters of this potential are determined on the basis of spectroscopic data for hadrons and results of lattice QCD calculations. We argue that the account of the U(1,3) symmetry is important for a description of strong interactions of quarks and gluons in a nonperturbative QCD domain at large interaction distances.

Motivation & Objective

• To incorporate quark and gluon confinement into nonperturbative QCD using a generalized space-time symmetry.
• To address the lack of a fundamental mechanism for confinement in standard QCD despite its experimental observation.
• To derive a universal confining potential from U(1,3) symmetry in complex phase space.
• To connect the potential's parameters with empirical data from hadron spectroscopy and lattice QCD calculations.

Proposed method

• Formalism based on U(1,3) group transformations in a complexified four-dimensional phase space C₄, defined via complex coordinates c_μ = q_μ − iκ⁻¹p_μ.
• Construction of U(1,3)-invariant Dirac-type equations for generalized quark fields using Grassmann algebra and covariant derivatives.
• Derivation of a scalar confining potential V_S(r) = √(m_C² + κ²r²) from the U(1,3) invariant structure, with r = |q_i − Q|.
• Use of simultaneous approximation in bound state calculations, imposing P^μq_1μ = P^μq_2μ = ... = P^μQ_μ to define the rest frame potential.
• Combines the U(1,3) scalar potential with a quasi-Coulombic vector potential V(r) = −4α_s/3r to form a total static potential V_tot(r).
• Expansion of the scalar potential at large r to identify the L"uscher term as (m_C1² + m_C2²)/(σr), linking it to lattice QCD predictions.

Experimental results

Research questions

• RQ1 Can U(1,3) symmetry in complex phase space provide a fundamental mechanism for quark and gluon confinement in nonperturbative QCD?
• RQ2 What are the quantitative parameters of the confining potential derived from U(1,3) symmetry, and how do they match experimental and lattice QCD data?
• RQ3 Does the U(1,3)-invariant scalar potential reproduce known features of confinement, such as linear growth and the L"uscher term?
• RQ4 How does the U(1,3) symmetry ensure Lorentz invariance and flavor independence of the confining potential?
• RQ5 Can the U(1,3) framework unify the description of confinement with existing potential models and string theory concepts?

Key findings

• The U(1,3) symmetry in complex phase space yields a scalar confining potential V_S(r) = √(m_C² + κ²r²) that grows linearly at large distances with slope κ.
• The string tension σ is determined to be σ = κ = 0.20 ± 0.02 GeV², consistent with lattice QCD and hadron spectroscopy.
• The confinement mass parameter m_c is found to be 0.45 ± 0.02 GeV, corresponding to the scale at which hadron formation becomes significant.
• The expansion of the scalar potential at large r includes a term (m_C1² + m_C2²)/(σr), which matches the L"uscher term predicted by lattice QCD when m_C1² + m_C2² = −πσ/12.
• The total static potential V_tot(r) combines a quasi-Coulombic vector part with the U(1,3)-invariant scalar potential, providing a unified description of short- and long-distance interactions.
• The confining potential is Lorentz-invariant and flavor-independent, supporting its role as a universal mechanism in nonperturbative QCD.