Trivial vacua, high orders in perturbation theory, and nontrivial condensates

Journal Article · Mon Jan 01 04:00:00 EST 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.53.933· OSTI ID:277483

Burkardt, M ^[1]

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1. Physics Department, New Mexico State University, Las Cruces, New Mexico 88003-0001 (United States)

In the limit of an infinite number of colors, an analytic expression for the quark condensate in (1+1)-dimensional (QCD{sub 1}{sub +}{sub 1}) is derived as a function of the quark mass and the gauge coupling constant. The vacuum condensate is perfectly well defined and is not zero for arbitrary {ital m}{sub {ital q}} despite the fact that the perturbative contribution is divergent. This calculation explicitly demonstrates the definition of the nonperturbative vacuum condensates. For zero quark mass, a nonvanishing quark condensate is obtained. Nevertheless, it is shown that there is no phase transition as a function of the quark mass in the {close_quote}t Hooft regime of the model. It is furthermore shown that the expansion of {l_angle}0{parallel}{bar {psi}}{psi}{parallel}0{r_angle} in the gauge coupling has zero radius of convergence but that the perturbation series is Borel summable with finite radius of convergence. The nonanalytic behavior {l_angle}0{parallel}{bar {psi}}{psi}{parallel}0{r_angle}{approximately}{sup {ital m}}{sub {ital q}}{r_arrow}0{minus}{ital N}{sub {ital c}} {radical}{ital G}{sup 2} can only be obtained by summing the perturbation series to infinite order. The sum-rule calculation is based on masses and coupling constants calculated from {close_quote}t Hooft{close_quote}s solution to QCD{sub 1}{sub +}{sub 1} which employs LF quantization and is thus based on a trivial vacuum. Nevertheless the chiral condensate remains nonvanishing in the chiral limit which is yet another example that semmingly trivial LF vacua are {ital not in conflict with QCD} {ital sum{minus}rule} results. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 277483
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 2 Vol. 53; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CONDENSATES
CONVERGENCE
COUPLING CONSTANTS
MASS
PERTURBATION THEORY
PHASE TRANSFORMATIONS
QUANTUM CHROMODYNAMICS
QUARKS
SUM RULES
TWO-DIMENSIONAL CALCULATIONS
VACUUM STATES