Quantum fluctuations of instantons in the nonlinear σ model

Fateev, V.A.; Frolov, I. V.; Schwarz, Albert

doi:10.1016/0550-3213(79)90367-5

Cited by 209 publications

(189 citation statements)

References 6 publications

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“…Contrary to the 4d YM theory, the instanton measure in that model is known exactly [33,34]. In the dilute limit the instanton measure reduces to the product of integrals over instanton sizes, positions and orientations, as in eq.…”

Section: Instanton Ensemblementioning

confidence: 99%

Instantons at work

Diakonov

2003

Progress in Particle and Nuclear Physics

352

506

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The aim of this review is to demonstrate that there exists a coherent picture of strong interactions, based on instantons. Starting from the first principles of Quantum Chromodynamics -via the microscopic mechanism of spontaneous chiral symmetry breakingone arrives to a quantitative description of the properties of light hadrons, with no fitting parameters. The discussion of the importance of instanton-induced interactions in soft high-energy scattering is new.

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Section: Instanton Ensemblementioning

confidence: 99%

Instantons at work

Diakonov

2003

Progress in Particle and Nuclear Physics

352

506

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“…[6] in case of N c = 2 (which is the O(3) sigma model) and in Refs. [7,8] for arbitrary CP Nc−1 ; the results of these references coincide up to notations.…”

Section: 'Zindons'mentioning

confidence: 99%

“…We have to conclude from this that the N c = 2 case is not a good system to be studied numerically. 6 The stability of the instanton-anti-instanton ensemble…”

Section: The Metropolis Algorithm and Regularization Proceduresmentioning

confidence: 99%

“…Contrary to the d = 4 Yang-Mills theory where the multi-instanton solutions are not available in an explicit form, in the CP Nc−1 model they are known explicitly, and for any 'number of colors' N c [4,5]. Moreover, the multi-instanton weight arising from integrating out quantum oscillations about instantons is also known [6,7,8]. In addition, the model is exactly solvable at large N c [5,9], and the spectrum is known for all N c [10].…”

Section: Introductionmentioning

confidence: 99%

“…Since the pioneering paper of Fateev, Frolov and Schwartz [6] it has been known that the multi-instanton system in the O(3) sigma model resembles that of a two-dimensional Coulomb plasma; it can be exactly bosonized to produce a sine-Gordon theory. In a true vacuum, however, one has both instantons and anti-instantons; such a system can be bosonized and solved exactly only at a specific value of the coupling [15] which may not be realistic.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On statistical mechanics of instantons in the CP−1 model

Diakonov

Maul

2000

Nuclear Physics B

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We introduce an explicit form of the multi-instanton weight including also instantonanti-instanton interactions for arbitrary N c in the two-dimensional CP Nc−1 model. To that end, we use the parametrization of multi-instantons in terms of instanton 'constituents' which we call 'zindons' for short. We study the statistical mechanics of zindons analytically (by means of the Debye-Hückel approximation) and numerically (running a Metropolis algorithm). Though the zindon parametrization allows for a complete 'melting' of instantons we find that, through a combination of dynamical and purely geometric factors, a dominant portion of topological charge is residing in well-separated instantons and anti-instantons.

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Skyrme Sphalerons of anO(3)-σ Model and the Calculation of Transition Rates at Finite Temperature

Zimmerschied

Tchrakian²,

Müller-Kirsten

1998

Fortschr. Phys.

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The reduced O(3)‐σ model with an O(3)‐σ→ O(2) symmetry breaking potential is considered with an additional Skyrmionic term, i.e. a totally antisymmetric quartic term in the field derivatives. This Skyrme term does not affect the classical static equations of motion which, however, allow an unstable sphaleron solution. Quantum fluctuations around the static classical solution are considered for the determination of the rate of thermally induced transitions between topologically distinct vacua mediated by the sphaleron. The main technical effect of the Skyrme term is to produce an extra measure factor in one of the flucuation path integrals which is therefore evaluated using a measuremodified Fourier‐Matsubara decomposition (this being one of the few cases permitting this explicit calculation). The resulting transition rate is valid in a temperature region different from that of the original Skyrme‐less model, and the crossover from transitions dominated by thermal fluctuations to those dominated by tunneling at the lower limit of this range depends on the strength of the Skyrme coupling.

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Quantum fluctuations of instantons in the nonlinear σ model

Cited by 209 publications

References 6 publications

Instantons at work

Instantons at work

On statistical mechanics of instantons in the CP−1 model

Skyrme Sphalerons of anO(3)-σ Model and the Calculation of Transition Rates at Finite Temperature

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