Stable Interactions Between the Extended Chern-Simons Theory and a Charged Scalar Field with Higher Derivatives: Hamiltonian Formalism (original) (raw)

Higher derivative extensions of 3d Chern–Simons models: conservation laws and stability

The European Physical Journal C, 2015

We consider the class of higher derivative 3d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.

Extension of the Chern–Simons Theory: Conservation Laws, Lagrange Structures, and Stability

Russian Physics Journal, 2017

We consider the class of higher derivative 3d vector field models with the wave operator being a polynomial of the Chern-Simons operator. For the nth order theory of this type, we provide a covariant procedure for constructing n-parameter family of conservation laws associated with spatiotemporal symmetries. This family includes the canonical energy that is unbounded from below, whereas others conservation laws from the family can be bounded from below for certain combinations of the Lagrangian parameters, even though higher derivatives are present in the Lagrangian. We prove that any conserved quantity bounded from below is related with invariance of the theory with respect to the time translations and ensures the stability of the model.

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

Physical Review D, 2012

A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [1], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons model as an example. A new Hamiltonian analysis of the model is provided. This Hamiltonian analysis has been used to construct the independent gauge generator. An exact mapping between the Hamiltonian gauge transformations and the U(1) symmetries of the action has been established.

Bounded Hamiltonian in the Fourth-Order Extension of the Chern–Simons Theory

Russian Physics Journal, 2018

The problem of constructing alternative Hamiltonian formulations in the extended Chern-Simons theory with higher derivatives is considered. It is shown that the fourth-order extended theory admits a four-parameter series of alternative Hamiltonians which can be bounded from below, even if the canonical energy of the model is unbounded from below.

Extended Chern–Simons Model for a Vector Multiplet

Symmetry, 2021

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 b...

COVARIANT LAGRANGIAN FORMALISM FOR CHERN-SIMONS THEORIES

International Journal of Geometric Methods in Modern Physics, 2007

We review the global formalism for Chern-Simons theories. Superpotentials are computed and the relation between the global Chern-Simons Lagrangian and the augmented variational principle is investigated.

The dynamical structure of higher dimensional Chern-Simons theory

Nuclear Physics B, 1996

Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry out the complete Dirac Hamiltonian analysis (separation of first and second class constraints and calculation of the Dirac bracket) for a group G × U (1). We also study the algebra of surface charges that arise in the presence of boundaries and show that it is isomorphic to the WZW 4 discussed in the literature. Some applications are then considered. It is shown, in particular, that Chern-Simons gravity in dimensions greater than or equal to five has a propagating torsion.

Hamiltonian reduction of the higher derivative Maxwell-Chern-Simons-Proca model

We consider a higher derivative model described by a Lagrangian action containing three terms, a Maxwell term, a third derivative extension of the Chern-Simons term and a Proca mass term. The Hamiltonian analysis of the model displays a second-class constraints set. A Hamiltonian reduction of the model is achieved and the connection to the extended Maxwell-Chern-Simons model is investigated.

Hamiltonian study for Chern-Simons and Pontryagin theories

Annals of Physics, 2011

The Hamiltonian analysis for the Chern-Simons theory and Pontryagin invariant, which depends of a connection valued in the Lie algebra of SO(3, 1), is performed. By applying a pure Dirac's method we find for both theories the extended Hamiltonian, the extended action, the constraint algebra, the gauge transformations and we carry out the counting of degrees of freedom. From the results obtained in the present analysis, we will conclude that the theories under study have a closed relation among its constraints and defines a topological field theory. In addition, we extends the configuration space for the Pontryagin theory and we develop the Hamitonian analysis for this modified version, finding a best description of the results previously obtained.

Higher derivative CP(N) model and quantization of the induced Chern-Simons term

Physical Review D, 2000

We consider higher derivative CP(N) model in 2 + 1 dimensions with the Wess-Zumino-Witten term and the topological current density squared term. We quantize the theory by using the auxiliary gauge field formulation in the path integral method and prove that the extended model remains renormalizable in the large N limit. We find that the Maxwell-Chern-Simons theory is dynamically induced in the large N effective action at a nontrivial UV fixed point. The quantization of the Chern-Simons term is also discussed.