On Critical Coupling Constants in Chiral Symmetry Breaking
Oct, 1982
24 pages
Published in:
- Phys.Rev.D 28 (1983) 1530
Report number:
- LPTHE-82-28
Citations per year
Abstract: (APS)
Finger, Horn, and Mandula showed in a Tamm-Dancoff approximation in QCD that Coulomb exchange induces instability of the chiral-invariant vacuum for αs>αscrit in the sense that for αs>αscrit there are negative eigenvalues of an operator H derived by them. We show here that another critical coupling constant αs′crit>αscrit is more meaningful. For αs>αs′crit there is no positive self-adjoint extension of H; for αs<αs′crit there is at least one; when αscrit<αs<αs′crit, among several self-adjoint extensions, a positive one is singled out by the physical requirement of a finite kinetic-energy expectation value. Considering, respectively, Coulomb exchange with the Tamm-Dancoff approximation, Coulomb exchange with the Bogoliubov-Valatin approximation, and Coulomb exchange plus transverse-gluon exchange, the values are 43αs′crit=8π(4+π2), 4π, 125π, to be compared with 43αscrit=32, 1, π(3π−4).- COUPLING CONSTANT: STRONG INTERACTION
- STRONG INTERACTION: COUPLING CONSTANT
- QUANTUM CHROMODYNAMICS
- GAUGE FIELD THEORY: CRITICAL PHENOMENA
- SYMMETRY BREAKING: CHIRAL
- EXCHANGE: COULOMB
- COULOMB: EXCHANGE
- GLUON: EXCHANGE
- EXCHANGE: GLUON
- APPROXIMATION: EFFECTIVE POTENTIAL
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