2007/02/07 by John M. Cornwall · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.76.025012
published as Phys.Rev.D76:025012,2007 · 15 pages, no figures, revtex4
arxiv created 2007/02/07 · openalex publication_date 2007/07/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Schr"odinger wave functional \ensuremathψ=exp(\ensuremath-SAia(\stackrel\ensuremath→x)) for the d=3+1 QCD vacuum is a partition function constructed in d=4; the exponent 2S [in |\ensuremathψ|2=exp(\ensuremath-2S)] plays the role of a d=3 Euclidean action. We start from a simple conjecture for S based on dynamical generation of a gluon mass M in d=4, then use earlier techniques of the author to extend (in principle) the conjectured form to full non-Abelian gauge invariance. We argue that the exact leading term, of O(M), in an expansion of S in inverse powers of M is a d=3 gauge-invariant mass term (gauged nonlinear sigma model); the next-leading term, of O(1/M), is a conventional Yang-Mills action. The d=3 action that is (twice) the sum of these two terms has center vortices as classical solutions. The d=3 gluon mass m3, which we constrain to be the same as M, and d=3 coupling g32 are related through the conjecture to the d=4 coupling strength, but at the same time the dimensionless ratio m3/g32 can be estimated from d=3 dynamics. This allows us to estimate the d=4 coupling \ensuremathαs(M2) in terms of the strictly d=3 ratio m3/g32; we find a value of about 0.4, in good agreement with an earlier theoretical value but somewhat low compared to the QCD phenomenological value of 0.7\ifmmode±\else\textpm\fi0.3. The wave functional for d=2+1 QCD has an exponent that is a d=2 infrared-effective action having both the gauge-invariant mass term and the field-strength squared term, and so differs from the conventional QCD action in two dimensions, which has no mass term. This conventional d=2 QCD would lead in d=3 to confinement of all color-group representations. But with the mass term (again leading to center vortices), only N\mathrm\text\ensuremath-ality\ensuremath\not≡0 mod N representations can be confined [for gauge group SU(N)], as expected.