From constrained stochastic processes to the nonlinear sigma model. Two old problems revisited

Ferrari, Franco

doi:10.1016/j.nuclphysb.2011.09.006

Cited by 1 publication

(3 citation statements)

References 50 publications

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“…[21], in which six non-Abelian Chern-Simon fields are necessary in order to reproduce the exponent e −iλτ 3 (C 1 ,C 2 ,C 3 ) , where τ 3 (C 1 , C 2 , C 3 ) is the Massey type invariant of Eq. (43). Moreover, in the present approach the introduction of non-local gauge invariant and metric independent operators like those of Ref.…”

Section: Discussionmentioning

confidence: 96%

“…(1) and the Massey invariant of Eq. (43). The final field theoretical models are respectively given in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…There are only a few techniques that have been developed in order to cope with theories containing delta functions, see e. g. Refs. [43,44,45]. A perturbative approach should also be possible.…”

Section: Discussionmentioning

confidence: 99%

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A new strategy to microscopic modeling of topological entanglement in polymers based on field theory

Ferrari

2019

Nuclear Physics B

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In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of the so-called numerical topological invariants. For each invariant it is possible to derive a field theory that describes the statistical behavior of knotted and linked polymer rings following a straightforward algorithm. The treatment is not limited to the partition function of the system, but it allows also to express the expectation values of general observables as field theory amplitudes.Our strategy is illustrated taking as examples the Gauss linking number and a topological invariant belonging to a class of invariants due to Massey. The consistency of the new method developed here is checked by reproducing a previous field theoretical model of two linked polymer rings. After the passage to field theory, the original topological constraints imposed on the fluctuating paths of the polymers become constraints over the configurations of the topological fields that mediate the interactions of topological origin between the monomers. These constraints involve quantities like the crosshelicity which are of interest in other disciplines, like for instance in modeling the solar magnetic field.While the calculation of the expectation values of generic observables remains still challenging due to the complexity of the problem of topological entanglement in polymer systems, we succeed here to reduce the evaluation of the moments of the Gauss linking number for two linked polymer rings to

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Section: Discussionmentioning

confidence: 96%

“…(1) and the Massey invariant of Eq. (43). The final field theoretical models are respectively given in Eq.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

A new strategy to microscopic modeling of topological entanglement in polymers based on field theory

Ferrari

2019

Nuclear Physics B

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From constrained stochastic processes to the nonlinear sigma model. Two old problems revisited

Cited by 1 publication

References 50 publications

A new strategy to microscopic modeling of topological entanglement in polymers based on field theory

A new strategy to microscopic modeling of topological entanglement in polymers based on field theory

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