Dual equivalence between self-dual and Maxwell–Chern–Simons models coupled to dynamical U(1) charged matter

Anacleto, M. A.; Ilha, Anderson; Nascimento, J. R.; Ribeiro, Ricardo Faria; Wotzasek, C.

doi:10.1016/s0370-2693(01)00300-8

Cited by 78 publications

(174 citation statements)

References 19 publications

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“…There are some approaches to perform such a conversion, like BFT method [30][31][32][33][34], the symplectic formalism [25,[35][36][37], and the Noether dualization technique [38][39][40]. As we mentioned before, in order to gauge a system with second-class constraints, we use the symplectic approach in order to embed a non-invariant system in an extended phasespace [41][42][43].…”

Section: Gauge Theories and Constraintsmentioning

confidence: 99%

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Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Nejad

Dehghani

Monemzadeh

2018

J. High Energ. Phys.

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Abstract:We study the effect of the simplest geometry which is imposed via the topology of the universe by gauging non-relativistic particle model on torus and 3-torus with the help of symplectic formalism of constrained systems. Also, we obtain generators of gauge transformations for gauged models. Extracting corresponding Poisson structure of existed constraints, we show the effect of the shape of the universe on canonical structure of phase-spaces of models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of extra dimensions in the phase-spaces of gauged embedded models are exactly two. Moreover, in classical form, we talk over modification of Newton's second law in order to study the origin of the terms appeared in the gauged theory.

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Section: Gauge Theories and Constraintsmentioning

confidence: 99%

“…In order to make another first-order constraint we should redefine them like (2.50), 38) whichΦ (0) 1 andΦ 3 are first-class, andΦ (1) 1 andΦ (1) 2 are second-class constraints. Now, we can make the canonical Hamiltonian,…”

Section: Jhep01(2018)017mentioning

confidence: 99%

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Nejad

Dehghani

Monemzadeh

2018

J. High Energ. Phys.

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“…These features are characteristics of Chern-Simons dualities involving matter coupling [18,4] ACKNOWLEDGMENTS: This work is partially supported by CNPq, PRONEX, CAPES, FAPERJ and FUJB, Brazilian Research Agencies. CW thanks the Physics Department of UFPB for the kind hospitality at the beginning of this investigation.…”

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confidence: 99%

“…Kk, 11.10.Lm, 11.10.Cd This work is devoted to the study of duality symmetry in the context of the Born-Infeld-Chern-Simons (BICS) theory [1], a generalization of the self-dual and Maxwell-Chern-Simons (MCS) duality, firstly shown by Deser and Jackiw [2] long time ago using the formalism of master Lagrangian. To this end we shall adopt a new gauge embedding formalism [3,4] that is alternative to the master Lagrangian approach.Duality deals with the equivalence between models that describe the same physical phenomenon. This is a symmetry that is playing an important role in nowadays physics.…”

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On the dual equivalence of the Born–Infeld–Chern–Simons model coupled to dynamical U(1) charged matter

Bazeia¹,

Ilha²,

Nascimento³

et al. 2001

Physics Letters B

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We study the equivalence between a nonlinear self-dual model (NSD) with the Born-InfeldChern-Simons (BICS) theory using an iterative gauge embedding procedure that produces the duality mapping, including the case where the NSD model is minimally coupled to dynamical, U(1) charged fermionic matter. The duality mapping introduces a current-current interaction term while at the same time the minimal coupling of the original nonlinear self-dual model is replaced by a non-minimal magnetic like coupling in the BICS side.PACS numbers: 11.10. Kk, 11.10.Lm, 11.10.Cd This work is devoted to the study of duality symmetry in the context of the Born-Infeld-Chern-Simons (BICS) theory [1], a generalization of the self-dual and Maxwell-Chern-Simons (MCS) duality, firstly shown by Deser and Jackiw [2] long time ago using the formalism of master Lagrangian. To this end we shall adopt a new gauge embedding formalism [3,4] that is alternative to the master Lagrangian approach.Duality deals with the equivalence between models that describe the same physical phenomenon. This is a symmetry that is playing an important role in nowadays physics. It has received a spate of interest in recent research in diverse areas in field theory such as, supersymmetric gauge theories [5], string theories [6], sine-Gordon model [7], statistical systems [8] and, in the context of condensed matter models, applied for instance to planar high-T C materials, Josephson junction arrays [9] and Quantum Hall Effect [10]. The existence of such a symmetry within a model may well have interesting consequences -it can be used to derive (exact) non perturbative results since swapping opposite coupling constant regimes allows a perturbative investigation of theories with large coupling constants. Moreover, it may be used to obtain information on the corresponding phase diagram, as it has been done in [8] where the relevant duality symmetry has been related to the modular group which, in that context, can be viewed as a generalization of the old Z 2 Kramers-Wannier duality of the 2-dimensional Ising model.Another possibility, which is closely related to our interest here, is the odd-dimensional duality involving ChernSimons term (CST) [11], whose paradigm is the equivalence between Self-Dual and Maxwell-Chern-Simons theories in (2+1) dimensions. This is a very special situation since the presence of the topological and gauge invariant ChernSimons term is responsible for the essential features manifested by the three dimensional field theories, such as parity breaking and anomalous spin. It produces deep insights in unrelated areas in particle physics and condensed matter both from the theoretical and phenomenological points of view [12], as mentioned above. The high temperature asymptotic of four dimensional field theory models and the understanding of the universal behavior of the Hall conductance in interacting electron systems also stand as important illustrations of this topic.Investigations of duality equivalence in D=3 involving CST has had a long history. I...

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Obtaining gauge invariant actions via symplectic embedding formalism

et al. 2012

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The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non-invariant ones. Both are named also as first- and second-class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non-invariant theories. Once established, this kind of mapping between first-class (gauge invariant) and second-class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non-invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non-Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non-Abelian systems.Comment: 20 pages. Two-column format. Final version to appear in Annalen der Physik. arXiv admin note: substantial text overlap with arXiv:1001.2254, arXiv:hep-th/010908

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Dual equivalence between self-dual and Maxwell–Chern–Simons models coupled to dynamical U(1) charged matter

Cited by 78 publications

References 19 publications

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

On the dual equivalence of the Born–Infeld–Chern–Simons model coupled to dynamical U(1) charged matter

Obtaining gauge invariant actions via symplectic embedding formalism

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