A remark on the effective action method in dynamics of vortices

Arodź, Henryk; Węgrzyn, Paweł

doi:10.1016/0370-2693(92)91040-g

Cited by 11 publications

(17 citation statements)

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“…The relations inverse to (43), (44) have the form also B (1) = 0 as it follows from Eq. (32) with the initial conditions (24). In general, Eq.…”

Section: Equation Of Motion For the Corementioning

confidence: 99%

“…Equations of motion contain higher derivatives with respect to time and consequently they have unphysical runaway type solutions. Moreover, it seems that the effective models should be nonlocal, see [24] where caveats concerning this approach are presented and Section 4 of the present paper.…”

Section: Introductionmentioning

confidence: 96%

“…Our perturbative scheme with the initial conditions (24) gives the basic curved domain wall. In Section 5 we discuss more general solutions obtained by adopting more general than (24) initial data for the B (n) fields.…”

mentioning

confidence: 99%

“…where χ (0) , ψ 0 are given by formulas (15), (22), χ (n) are given by formula (27), and B (1) , B (3) are solutions of Eqs. (32), (35) with the initial data (24). Before solving Eqs.…”

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confidence: 99%

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Expansion in the width and collective dynamics of a domain wall

Arodź

1998

Nuclear Physics B

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We show that collective dynamics of a curved domain wall in a (3+1)-dimensional relativistic scalar field model is represented by Nambu-Goto membrane and (2+1)-dimensional scalar fields defined on the worldsheet of the membrane. Our argument is based on a recently proposed by us version of the expansion in the width. Derivation of the expansion is significantly reformulated for the present purpose. Third and fourth order corrections to the domain wall solution are considered. We also derive an equation of motion for the core of the domain wall. Without the (2+1)-dimensional scalar fields this equation would be nonlocal.

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“…The relations inverse to (43), (44) have the form also B (1) = 0 as it follows from Eq. (32) with the initial conditions (24). In general, Eq.…”

Section: Equation Of Motion For the Corementioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

mentioning

confidence: 99%

“…where χ (0) , ψ 0 are given by formulas (15), (22), χ (n) are given by formula (27), and B (1) , B (3) are solutions of Eqs. (32), (35) with the initial data (24). Before solving Eqs.…”

mentioning

confidence: 99%

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Expansion in the width and collective dynamics of a domain wall

Arodź

1998

Nuclear Physics B

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“…The price for this is that the membrane is no longer of the Nambu-Goto type. Effective action for such membrane contains higher derivatives with respect to time, and probably is nonlocal [6]. The reason for these unpleasant features is that the points at which the scalar field vanishes do not constitute a physical object (the physical object is the domain wall itself and not the core), and therefore the core, being a purely mathematical construct, can have strange from the physical point of view equation of motion.…”

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confidence: 99%

Collective Dynamics of a Domain Wall — an Outline

Arodź¹

NATO Science Series: B:

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We shall consider domain walls in a relativistic field-theoretical model defined by the following Lagrangianwhere Φ is a single real scalar field, (η µν )=diag(-1,1,1,1) is the metric in Minkowski space-time, and λ, M are positive parameters. Euler-Lagrange equation corresponding to Lagrangian (1) has the particular time-independent solutionwhich describes a static, planar domain wall stretched along the x 3 = 0 plane. Here Φ 0 = M/(2 √ λ) denotes one of the two vacuum values of the field Φthe other one is equal to −Φ 0 . The parameter M can be identified with the mass of the scalar particle related to the field Φ. The corresponding Compton length l 0 = M −1 gives the physical length scale in the model. Energy density for the planar domain wall (2) is exponentially localised in a vicinity of the x 3 = 0 plane. The transverse width of the domain wall is of the order 2l 0 .The issue is time evolution of a non-planar domain wall. Such domain walls can be infinite, consider, e.g., locally deformed planar domain wall or a cylindrical domain wall. They can also be finite closed, e.g., like a sphere or a torus. We shall restrict our considerations to a single large, smooth 1

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Evolution of Local Vortices and Interfaces

Arodź

2003

Patterns of Symmetry Breaking

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A remark on the effective action method in dynamics of vortices

Cited by 11 publications

References 11 publications

Expansion in the width and collective dynamics of a domain wall

Expansion in the width and collective dynamics of a domain wall

Collective Dynamics of a Domain Wall — an Outline

Evolution of Local Vortices and Interfaces

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