Untwisting twisted 
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 kinks by a bare fermion mass

Thies, Michael

doi:10.1103/physrevd.96.116018

Cited by 5 publications

(9 citation statements)

References 22 publications

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“…Twist can then only survive in the sense of intermediate asymptotics, as was found in Ref. [17]. We propose to use once again the trick with the local chiral rotation as follows: Suppose we have found a HF solution in the infinite volume with total twist angle ϕ,…”

Section: A Simple Infrared Regularizationmentioning

confidence: 97%

“…Recently, an attempt was made to extend the twisted kinks to finite bare fermion masses [17]. Due to technical difficulties, this could only be done in the non-relativistic limit so far, i.e., for small occupation fraction and smooth shapes.…”

Section: Why Infrared Problems?mentioning

confidence: 99%

“…Unlike the results for finite fermion mass in Ref. [17], this construction applies to any twist angle ϕ ∈ [0, π]. Let us check more quantitatively the picture that a NJL 2 baryon is a twisted kink glued to an incomplete winding of the chiral spiral.…”

Section: Application To the Twisted Kinkmentioning

confidence: 99%

“…Unlike the results for finite fermion mass in Ref. [17], this construction applies to any twist angle ϕ ∈ [0, π].…”

Section: Application To the Twisted Kinkmentioning

confidence: 99%

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Fermion number of twisted kinks in the NJL2 model revisited

Thies

2018

Phys. Rev. D

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As a consequence of axial current conservation, fermions cannot be bound in localized lumps in the massless Nambu-Jona-Lasinio model. In the case of twisted kinks, this manifests itself in a cancellation between the valence fermion density and the fermion density induced in the Dirac sea. To attribute the correct fermion number to these bound states requires an infrared regularization. Recently, this has been achieved by introducing a bare fermion mass, at least in the nonrelativistic regime of small twist angles and fermion numbers. Here, we propose a simpler regularization using a finite box which preserves integrability and can be applied at any twist angle. A consistent and physically plausible assignment of fermion number to all twisted kinks emerges. DOI: 10.1103/PhysRevD.97.056012 I. WHY INFRARED PROBLEMS?Consider the Nambu-Jona-Sums over N flavors are suppressed as usual (ψψ ¼ P N k¼1ψ k ψ k , etc.). Since the Lagrangian (1) features only zero-range interactions, one would expect ultraviolet (UV) rather then infrared (IR) problems. Indeed, in 3 þ 1 dimensions this theory is not renormalizable. In 1 þ 1 dimensions, UV problems are harmless and can be handled by a mere renormalization of the coupling constant. In order to understand the origin of possible IR problems, we have to remember that the NJL 2 model possesses a continuous U(1) chiral symmetry,Strictly speaking, a continuous symmetry cannot be broken spontaneously in 1 þ 1 dimensions [3,4]. However, in the large-N limit, mean field theory is believed to become exact so that one may envisage the spontaneous breakdown of chiral symmetry in the NJL 2 model [5,6]. The appropriate mean-field approach for fermions is the Hartree-Fock (HF)or time-dependent Hartree-Fock approximation. In the relativistic version needed here, one starts from the Dirac equationThe scalar (S) and pseudoscalar (P) potentials obey the self-consistency conditionsThe sum over all occupied orbits includes the Dirac sea and possible occupied positive energy levels. The vacuum corresponds to the solution of Eqs. (3)- (4) with homogeneous S, P. It is infinitely degenerate and characterized by a chiral vacuum angle θ,The U(1) manifold of all possible vacua is called the chiral circle. Its radius is the dynamical fermion mass m, generated by dimensional transmutation from a dimensionless coupling constant via the vacuum gap equation [2,7] πSpontaneous symmetry breaking now amounts to picking one point on the chiral circle, say, Δ ¼ m, as vacuum.Computing small fluctuations around the vacuum with the relativistic random phase approximation yields the information about the meson spectrum. One finds a massive, scalar σ meson (m σ ¼ 2m) and a massless, pseudoscalar π

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Section: A Simple Infrared Regularizationmentioning

confidence: 97%

Section: Why Infrared Problems?mentioning

confidence: 99%

Section: Application To the Twisted Kinkmentioning

confidence: 99%

“…Unlike the results for finite fermion mass in Ref. [17], this construction applies to any twist angle ϕ ∈ [0, π].…”

Section: Application To the Twisted Kinkmentioning

confidence: 99%

See 2 more Smart Citations

Fermion number of twisted kinks in the NJL2 model revisited

Thies

2018

Phys. Rev. D

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“…We have already mentioned that the full charge density vanishes due to a cancellation between continuum and bound states, a consequence of chiral symmetry and current conservation. In the one flavor case, it was recently pointed out that the total charge of a twisted kink is infrared sensitive and needs some regularization, either by a small bare fermion mass [18] or a finite box [19]. The conclusion was that the charge is spread out over the whole space in the thermodynamic and chiral limit and hence becomes invisible.…”

Section: Example I: Single Twisted Kinkmentioning

confidence: 99%

Twisted kink dynamics in multiflavor chiral Gross-Neveu model

Thies

2021

Preprint

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The Gross-Neveu model with UL(N f ) × UR(N f ) chiral symmetry is reconsidered in the large Nc limit. The known analytical solution for the time dependent interaction of any number of twisted kinks and breathers is cast into a more revealing form. The (x, t)-dependent factors are isolated from constant coefficients and twist matrices. These latter generalize the twist phases of the single flavor model. The crucial tool is an identity for the inverse of a sum of two square matrices, derived from the known formula for the determinant of such a sum.

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Twisted kink dynamics in multiflavor chiral Gross–Neveu model

Thies

2021

J. Phys. A: Math. Theor.

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The Gross-Neveu model with UL(Nf)xUR(Nf) chiral symmetry is reconsidered in the large Nc limit. The known analytical solution for the time dependent interaction of any number of twisted kinks and breathers is cast into a more revealing form. The (x,t)-dependent factors are isolated from constant coefficients and twist matrices. These latter generalize the twist phases of the single flavor model. The crucial tool is an identity for the inverse of a sum of two square matrices, derived from the known formula for the determinant of such a sum.

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Untwisting twisted NJL2 kinks by a bare fermion mass

Cited by 5 publications

References 22 publications

Fermion number of twisted kinks in the NJL2 model revisited

Fermion number of twisted kinks in the NJL2 model revisited

Twisted kink dynamics in multiflavor chiral Gross-Neveu model

Twisted kink dynamics in multiflavor chiral Gross–Neveu model

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