Semiclassical bound states in an asymptotically free theory

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

doi:10.1103/physrevd.12.2443

Cited by 377 publications

(561 citation statements)

References 12 publications

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“…Mathematically, we thus have to let C enclose the cut on the negative ω axis and then go around the pole at −ω b N times and around the pole at ω b N f times. In this way, we obtain [6,8] …”

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confidence: 99%

“…Note that M(1, 0) = 2N m π is the kink-antikink threshold of the GN model [8]. It appears that the logarithmic singularity in M(1, γ) is associated with the enhanced Z 2 symmetry at γ = 0.…”

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confidence: 99%

“…The GN model contains a soliton (the so called CCGZ kink [7,8,6]) in which the σ field takes on equal and opposite values at x = ±∞. The stability of this soliton is obviously guaranteed by topological considerations.…”

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confidence: 99%

“…Further substituting σ(x) as given in (9) configurations, all of them are reflectionless, with a single bound state [6,7,8], or more [10].…”

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confidence: 99%

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Fermion bags in the massive Gross-Neveu model

Feinberg

Zee

1997

Physics Letters B

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As has long been known, it is energetically favorable for massive fermions to deform the homogeneous vacuum around them, giving rise to extended bag-like objects. We study this phenomenon non-perturbatively in a model field theory, the 1+1 dimensional Massive Gross-Neveu model, in the large N limit. We prove that the bags in this model are necessarily time dependent. We calculate their masses variationally and demonstrate their stability. We find a non-analytic behavior in these masses as we approach the standard massless Gross-Neveu model and argue that this behavior is caused by the kink-antikink threshold. This work extends our previous work to a non-integrable field theory.

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confidence: 99%

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confidence: 99%

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confidence: 99%

“…Further substituting σ(x) as given in (9) configurations, all of them are reflectionless, with a single bound state [6,7,8], or more [10].…”

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confidence: 99%

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Fermion bags in the massive Gross-Neveu model

Feinberg

Zee

1997

Physics Letters B

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“…More generally, the interaction of fermions with solitonic backgrounds could produce or affect a variety of interesting physical phenomena such as charge and fermion number fractionalization [79][80][81][82][83], hadron physics [68,69,[84][85][86], superfluidity [87,88], superconductivity [89], BoseEinstein condensation [90,91], conducting polymers [83,[92][93][94] and localization of fermions [95][96][97][98]. The spectrum of the fermion can in general be distorted due to the presence of such a background; bound states can appear and continuum states can change as compared with the free fermion.…”

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confidence: 99%

An investigation of the Casimir energy for a fermion coupled to the sine-Gordon soliton with parity decomposition

2014

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We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities, i.e. the spectrum of the states and the phase shifts, for each parity channel, separately. We present and use a simple prescription to construct the simultaneous eigenstates of the Hamiltonian and parity in the continua from the scattering states. We also use a prescription we had introduced earlier to calculate unique expressions for the phase shifts and check their consistency with both the weak and the strong forms of the Levinson theorem. In the graphs of the total and parity decomposed Casimir energies as a function of the parameters of the pseudoscalar field distinctive deformations appear whenever a fermionic bound state energy level with definite parity crosses the line of zero energy. However, the latter graphs show considerable sensitivity to the fine details of the shape of the background field which cannot be seen from the graph of the total Casimir energy. Finally, we consider a system consisting of a valence fermion in the ground state and find that the most energetically favorable configuration is the one with a soliton of winding number one, and this conclusion does not hold for each parity, separately.

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