Solitons and Particles

Rebbi, C.; Soliani, G.

doi:10.1142/0046

Cited by 99 publications

(90 citation statements)

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“…: µ means normal ordering at the scale µ and Λ is the ultra-violet cut-off. The expression (2.4) is a trivial consequence of the perturbative derivation of the vacuum expectation value of the operator cos βϑ(x) 5) where D (+) (x; µ) is the two-point Wightman function defined by…”

Section: Introductionmentioning

confidence: 99%

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Faber

Ivanov²

2003

J. Phys. A: Math. Gen.

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We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088Rev. D 11, (1975. According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants β 2 > 8π. The consequence of this theorem would be the non-existence of the quantum ground state of the sineGordon model for β 2 > 8π. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for β 2 > 8π. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model. *

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Section: Introductionmentioning

confidence: 99%

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Faber

Ivanov²

2003

J. Phys. A: Math. Gen.

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“…Observe first that whenever a weakly recursive flow is Hamiltonian, with a differential operator in x as implectic operator (see [10], [4] for definitions), then this flow is completely integrable. This is easily seen, take the coefficients of the characteristic operator, then evaluation of each coefficient at any x gives a conserved quantity.…”

Section: Further Applicationsmentioning

confidence: 99%

Nilpotent and recursive flows

Fuchssteiner

Schiavo

1993

Manuscripta Math

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In this paper we introduce a class of nonlinear vector fields on infinite dimensional manifolds such that the corresponding evolution equations can be solved with the same method one uses to solve ordinary differential equations with constant coefficients. Mostly, these equations are nonlinear partial differential equations. It is shown that these flows are characterized by a generalization of the 'method of variation of constants' which is widely used for second order problems to find general solutions out of particular ones. Invariant densities are constructed for these flows in a natural way. These invariant densities are providing an essential tool for solving initial value and boundary value problems for the equations under consideration. Many applications are presented

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“…Such solutions were obtained in exact analytical form for a variety of models including Quantum Chromo Dynamics (QCD). They have been considered as configurations of quantum fields that provide a tunnelling effect between the vacuums that have different topologies in space-time [3][4][5]. The name indicates that the fluctuations are confined to an instant in space-time [6].…”

Section: Introductionmentioning

confidence: 99%

The Effect of Bichromatic Potential on Thirring Instantons

Aydoğmuş¹

2017

deufmd

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Özet:Thirring model is a 2D conformally invariant pure fermionic model with no mass term. The model admits particle-like solutions and these solutions are instantonic in character. In this study, the effect of bichromatic potential on Thirring instantons is investigated to get a better idea of their nonlinear dynamical nature. For this purpose, the phase portraits are constructed. Under some parameter conditions, chaos is observed. Bikromatik Potansiyelin Thirring İnstantonları Üzerine EtkisiKeywords Soliton, İnstanton, Bikromatik, Lineer olmayan dinamik. Abstract:Thirring model iki boyutlu konformal invaryant kütlesiz saf bir fermiyonik modeldir. Model parçacık benzeri çözümler sergiler ve bu çözümler instanton karakterindedir. Bu çalışmada Thirring instantonlarının lineer olmayan dinamiğini daha iyi kavrayabilmek için bikromatik potansiyelin model üzerindeki etkisi incelenmiştir. Bu amaçla faz portreleri inşa edilmiş ve bazı sistem parametre değerleri için kaos gözlemlenmiştir.

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Solitons and Particles

Cited by 99 publications

References 0 publications

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Nilpotent and recursive flows

The Effect of Bichromatic Potential on Thirring Instantons

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Solitons and Particles

Cited by 99 publications

References 0 publications

Is the energy density of the ground state of the sine-Gordon model unbounded from below for 2> 8 ?

Is the energy density of the ground state of the sine-Gordon model unbounded from below for 2> 8 ?

Nilpotent and recursive flows

The Effect of Bichromatic Potential on Thirring Instantons

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Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?