Gauge invariances of higher derivative Maxwell-Chern-Simons field theory: A new Hamiltonian approach

Mukherjee, Prerana; Paul, Biswajit

doi:10.1103/physrevd.85.045028

Cited by 36 publications

(37 citation statements)

References 74 publications

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“…of higher derivative theory following Cordero, Molgado and Rojas [4]. We have presented a new Hamiltonian formulation of the model based on the equivalent first-order formalism [11,27,28]. This is different from the analysis of [4], where the usual Ostrogradsky approach is adopted.…”

Section: Discussionmentioning

confidence: 99%

“…This paradox was resolved in [11] using the equivalent first-order approach, where a well-known algorithm for constructing the Hamiltonian gauge generator [25,26] was used along with conditions imposed due to the higher derivative nature. This additional constraint may or may not lead to an independent restriction on the gauge generator [11,27,28]. It did impose an independent additional restriction on the gauge invariances of the massive relativistic model with curvature which explained the apparent mismatch between the number of primary first class constraints and the number of independent gauge degrees of freedom mentioned above [11].…”

Section: Discussionmentioning

confidence: 99%

“…A Hamiltonian analysis of the same model has been discussed in [4] from the Ostrogradsky approach. We on the other hand adopt the equivalent firstorder formalism which has been demonstrated to be useful, specifically in treating the gauge invariances from the Hamiltonian point of view [11,27,28]. The point of departure is to convert (8) to a first-order theory by defining the first derivative of a and t as additional fields and including the following constraints into the Lagrangian with the help of undetermined multipliers.…”

Section: Hamiltonian Analysismentioning

confidence: 99%

See 2 more Smart Citations

New Hamiltonian analysis of Regge-Teitelboim minisuperspace cosmology

Banerjee

Mukherjee²,

Paul

2014

Phys. Rev. D

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A new Hamiltonian formulation of the minisuperspace cosmology following from the geodetic brane gravity model introduced by Regge and Teitelboim is presented. The model is considered in the framework of higher derivative theories which facilitates Hamiltonian formulation. The analysis is done using the equivalent first-order approach. The gauge generator containing the exact number of gauge parameters is constructed. Equivalence between the gauge and reparametrization symmetries has been demonstrated. Complete gauge fixed computations have been provided and formal quantization is done indicating the Wheeler DeWitt equation. Compatibility with existing results is shown.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Hamiltonian Analysismentioning

confidence: 99%

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New Hamiltonian analysis of Regge-Teitelboim minisuperspace cosmology

Banerjee

Mukherjee²,

Paul

2014

Phys. Rev. D

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“…In other contexts, θ ED under consideration here has been studied as a 3 þ 1 particular kind of Maxwell-Chern-Simons electrodynamics, where it has received considerable attention [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. And also it has been studied as a restricted subset of the Standard Model extension [32,33], where several results have been achieved, too [34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Electro- and magnetostatics of topological insulators as modeled by planar, spherical, and cylindricalθboundaries: Green’s function approach

2016

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The Green's function method is used to analyze the boundary effects produced by a Chern-Simons extension to electrodynamics. We consider the electromagnetic field coupled to a θ term that is piecewise constant in different regions of space, separated by a common interface Σ, the θ boundary, model which we will refer to as θ electrodynamics. This model provides a correct low-energy effective action for describing topological insulators. Features arising due to the presence of the boundary, such as magnetoelectric effects, are already known in Chern-Simons extended electrodynamics, and solutions for some experimental setups have been found with a specific configuration of sources. In this work we construct the static Green's function in θ electrodynamics for different geometrical configurations of the θ boundary, namely, planar, spherical and cylindrical θ-interfaces. Also, we adapt the standard Green's theorem to include the effects of the θ boundary. These are the most important results of our work, since they allow one to obtain the corresponding static electric and magnetic fields for arbitrary sources and arbitrary boundary conditions in the given geometries. Also, the method provides a well-defined starting point for either analytical or numerical approximations in the cases where the exact analytical calculations are not possible. Explicit solutions for simple cases in each of the aforementioned geometries for θ boundaries are provided. On the one hand, the adapted Green's theorem is illustrated by studying the problem of a pointlike electric charge interacting with a planar topological insulator with prescribed boundary conditions. On the other hand, we calculate the electric and magnetic static fields produced by the following sources: (i) a pointlike electric charge near a spherical θ boundary, (ii) an infinitely straight current-carrying wire near a cylindrical θ boundary and (iii) an infinitely straight uniformly charged wire near a cylindrical θ boundary. Our generalization, when particularized to specific cases, is successfully compared with previously reported results, most of which have been obtained by using the method of images.

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“…As the second term in the action (1) contains higher derivative terms ∂ λ ∂ λ A μ , the canonical analysis will be done by a variant of Ostrogradsky method [46][47][48][49][50][51] developed in Ref. [52], based on an equivalent first order formalism [53,54] and applied to a number of particle and field theoretic models [52,[55][56][57]. The Hamiltonian analysis of a higher derivative extension of a theory displays a constraints set with a more complicated structure than the constraints set of the usual theory (where the Lagrangian is a function of the fields and their first derivatives only).…”

Section: Introductionmentioning

confidence: 99%