Quantization of the higher derivative Maxwell–Chern–Simons–Proca model based on BFT method

Sararu, S. C.; Udriștioiu, Mihaela Tinca

doi:10.1142/s0217732316502059

Cited by 11 publications

(5 citation statements)

References 47 publications

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“…All the Poisson brackets between φ, π and A i , F i , G i vanish. The relations (69), ( 70), (71) can be obtained from (38), (39), (40), (41) after substitution (49). We note that the Poisson bracket between the fields A i , F i , W i is constant, even though the theory involves extra fields π, φ.…”

Section: A Uniqueness Of Consistent Interaction Vertexmentioning

confidence: 99%

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Extended Chern-Simons model for a vector multiplet

Kaparulin

Lyakhovich

Nosyrev

2021

Preprint

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We consider a gauge theory of vector fields in 3d Minkowski space. At the free level, the dynamical variables are subjected to the extended Chern-Simons (ECS) equations with higher derivatives. If the color index takes n values, the third-order model admits a 2n-parameter series of second-rank conserved tensors, which includes the canonical energy-momentum. Even though the canonical energy is unbounded, the other representatives in the series can have bounded from below 00-component. The theory admits consistent self-interactions with the Yang-Mills gauge symmetry. The Lagrangian couplings preserve the unbounded from below energy-momentum tensor, and they do not lead to a stable non-linear theory. The non-Lagrangian couplings are consistent with the existence of conserved tensor with a bounded from below 00-component. These models are stable at the non-linear level. The dynamics of interacting theory admits a constraint Hamiltonian form. The Hamiltonian density is given by the 00-component of the conserved tensor. In the case of stable interactions, the Poisson bracket and Hamiltonian do not follow from the canonical Ostrogradski construction. The particular attention is paid to the "triply massless" ECS theory, which demonstrates instability already at the free level. It is shown that the introduction of extra scalar field, serving as Higgs, can stabilize dynamics in the vicinity of the local minimum of energy. The equations of motion of stable model are non-Lagrangian, but they admit the Hamiltonian form of dynamics with a bounded from below Hamiltonian.

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Section: A Uniqueness Of Consistent Interaction Vertexmentioning

confidence: 99%

“…In the current studies, it is often serves as a prototype of the class of gauge theories with higher derivatives, see eg. [39][40][41]. The stability of the ECS model has been first studied in [33].…”

Section: Introductionmentioning

confidence: 99%

Extended Chern-Simons model for a vector multiplet

Kaparulin

Lyakhovich

Nosyrev

2021

Preprint

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“…Seminal applications of the BFFT formalism can be seen in references [26,27,28,29,30,31,32,33], while more recent accounts can be found in [34,35,36,37]. In [34], the authors show an interesting study of graphene in non-commutative space in which the BFFT formalism is used to recover broken gauge symmetries, whereas [35] deals with a constrained higher-order-derivatives model within the BFFT conversional approach. A direct application of the BFFT formalism to the non-Abelian supersymmetric Chern-Simons model can be seen in reference [36].…”

Section: Introductionmentioning

confidence: 99%

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

Pandey,

Thibes

2021

Preprint

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We apply the BFFT formalism to a prototypical second-class system, aiming to convert its constraints from second-to first-class. The proposed system admits a consistent initial set of second-class constraints and an open potential function providing room for applications to mechanical models as well as field theory such as the non-linear sigma model. The constraints can be arbitralily non-linear, broadly generalizing previously known cases. We obtain a sufficient condition for which a simple closed expression for the Abelian converted constraints and modified involutive Hamiltonian can be achieved. As explicit examples, we discuss a particle on a torus and a spontaneous Lorentz symmetry breaking vector model, obtaining in both situations the full first-class abelianized constraints in closed form and the corresponding involutive Hamiltonian.

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“…The ECS model [13] is the simplest gauge theory of the derived type. In current studies, it often serves as a prototype of the class of gauge theories with higher derivatives; see, e.g., [39][40][41]. The stability of the ECS model was first studied in [33].…”

Section: Introductionmentioning

confidence: 99%

Extended Chern–Simons Model for a Vector Multiplet

2021

View full text Add to dashboard Cite

We consider a gauge theory of vector fields in 3D Minkowski space. At the free level, the dynamical variables are subjected to the extended Chern–Simons (ECS) equations with higher derivatives. If the color index takes n values, the third-order model admits a 2n-parameter series of second-rank conserved tensors, which includes the canonical energy–momentum. Even though the canonical energy is unbounded, the other representatives in the series have a bounded from below the 00-component. The theory admits consistent self-interactions with the Yang–Mills gauge symmetry. The Lagrangian couplings preserve the energy–momentum tensor that is unbounded from below, and they do not lead to a stable non-linear theory. The non-Lagrangian couplings are consistent with the existence of a conserved tensor with a 00-component bounded from below. These models are stable at the non-linear level. The dynamics of interacting theory admit a constraint Hamiltonian form. The Hamiltonian density is given by the 00-component of the conserved tensor. In the case of stable interactions, the Poisson bracket and Hamiltonian do not follow from the canonical Ostrogradski construction. Particular attention is paid to the “triply massless” ECS theory, which demonstrates instability even at the free level. It is shown that the introduction of extra scalar field, serving as Higgs, can stabilize the dynamics in the vicinity of the local minimum of energy. The equations of motion of the stable model are non-Lagrangian, but they admit the Hamiltonian form of dynamics with a Hamiltonian that is bounded from below.

show abstract

Quantization of the higher derivative Maxwell–Chern–Simons–Proca model based on BFT method

Cited by 11 publications

References 47 publications

Extended Chern-Simons model for a vector multiplet

Extended Chern-Simons model for a vector multiplet

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

Extended Chern–Simons Model for a Vector Multiplet

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