Nonperturbative methods and extended-hadron models in field theory. I. Semiclassical functional methods

Dashen, Roger; Hasslacher, Brosl; Neveu, A.

doi:10.1103/physrevd.10.4114

Cited by 529 publications

(388 citation statements)

References 14 publications

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“…Ifh 2 is time independent and does not contain time derivatives, one has 20) where T limits the time integral. For a one-dimensional potential scattering problem, it can be shown [38] that the continuum part of the scattering operator's trace may be accounted for through a phaseshift integral. Using the hedgehog ansatz in the adiabatic approximation the e.o.m for the fluctuations (2.18) may be decomposed into partial waves [39] for which the one-dimensional phase shift formula applies.…”

Section: Continuum Contributions: the Phaseshift Formulamentioning

confidence: 99%

Quantum corrections to baryon properties in chiral soliton models

Meier¹,

Walliser²

1997

Physics Reports

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Chiral lagrangians as effective field theories of QCD are successfully applied to meson physics at low energies in the framework of chiral perturbation theory. Because of their nonlinear structure these lagrangians allow for static soliton solutions which may be interpreted as baryons. Their semiclassical quantization, which provides the leading order in an 1/N C expansion (N C is the number of colors) turned out to be insufficient in many cases to obtain good agreement with empirical baryon observables. However with N C = 3, large corrections are expected in the next-to-leading order which is carried by pionic fluctuations around the soliton background. The calculation of these corrections requires renormalization to 1-loop of the underlying field theory. We present a procedure to calculate the 1-loop contributions for a variety of baryonic observables. In contrast to chiral perturbation theory, terms with an arbitrary number of gradients may in principle contribute and the restriction to low chiral orders can only be justified by the investigation of the scale independence of the results. The results generally give the right sign and magnitude to reduce the discrepancy between theory and experiment with one exception: the axial quantities. These suffer from the fact that the underlying current algebra mixes different N C orders, which suggests a large and positive next-to-next-to-leading order contribution, which is probably sufficient to close the gap to experiment.

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Section: Continuum Contributions: the Phaseshift Formulamentioning

confidence: 99%

Quantum corrections to baryon properties in chiral soliton models

Meier¹,

Walliser²

1997

Physics Reports

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“…The fact that the model possesses exact periodic solutions bound to the boundary makes the stationary-phase method a suitable candidate for their quantisation. The method is based on the work of Dashen, Hasslacher and Neveu [12,13] for the semi-classical quantisation of the sine-Gordon model. In this case it appears as a generalised version of the Bohr-Sommerfeld quantisation rule…”

Section: Semi-classical Quantisationmentioning

confidence: 99%

Quantum complex sine-Gordon model on a half line

Bowcock

Tzamtzis

2007

J. High Energy Phys.

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In this paper, we examine the quantum complex sine-Gordon model on a half line. We obtain the quantum spectrum of boundary bound states using the the semiclassical method of Dashen, Hasslacher and Neveu. The results are compared and found to agree with the bootstrap programme. A particle/soliton reflection factor is conjectured, which is consistent with unitary, crossing and our semi-classical results.

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“…According to a theorem on functional determinants of ordinary differential operators [19,27,28] we can express the ratios of the partial wave determinants via…”

Section: Computation Of the Fluctuation Determinantmentioning

confidence: 99%

Erratum: False vacuum decay by self-consistent bounces in four dimensions [Phys. Rev. D75, 045001 (2007)]

Baacke¹,

Kevlishvili²

2007

Phys. Rev. D

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We compute bounce solutions describing false vacuum decay in a Φ 4 model in four dimensions with quantum back-reaction. The back-reaction of the quantum fluctuations on the bounce profiles is computed in the one-loop and Hartree approximations. This is to be compared with the usual semiclassical approach where one computes the profile from the classical action and determines the one-loop correction from this profile. The computation of the fluctuation determinant is performed using a theorem on functional determinants, in addition we here need the Green' s function of the fluctuation 1 e-mail: baacke@physik.uni-dortmund.de 2 e-mail: nina.kevlishvili@het.physik.uni-dortmund.de operator in oder to compute the quantum back-reaction. As we are able to separate from the determinant and from the Green' s function the leading perturbative orders, we can regularize and renormalize analytically, in analogy of standard perturbation theory. The iteration towards self-consistent solutions is found to converge for some range of the parameters. Within this range the corrections to the semiclassical action are at most a few percent, the corrections to the transition rate can amount to several orders of magnitude. The strongest deviations happen for large couplings, as to be expected. Beyond some limit, there are no self-consistent bounce solutions.2

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Nonperturbative methods and extended-hadron models in field theory. I. Semiclassical functional methods

Cited by 529 publications

References 14 publications

Quantum corrections to baryon properties in chiral soliton models

Quantum corrections to baryon properties in chiral soliton models

Quantum complex sine-Gordon model on a half line

Erratum: False vacuum decay by self-consistent bounces in four dimensions [Phys. Rev. D75, 045001 (2007)]

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