EXTENDED FADDEEV-JACKIW CANONICAL QUANTIZATION FOR THE (1+1)-DIMENSIONAL NONRELATIVISTIC ELECTRODYNAMICS

Some time ago, we proposed an extension of the usual Faddeev-Jackiw formalism for constrained systems with Grassmann dynamic variables in the field theory context. In the present work, we apply this extended formalism to the (1+1)-dimensional nonrelativistic electrodynamics. By comparing the obtained results with those corresponding to the implementation of Dirac formalism on this model, we find the same constraints and generalized brackets. In this way, we can conclude that the extended Faddeev-Jackiw and the Dirac formalisms can be considered equivalent, at least for this model. On the contrary, in this case, we find that there is no equivalence between the usual Faddeev-Jackiw and the Dirac formalisms. On the other hand, we observe that the extended formalism is more economical than the Dirac one regarding the computation of both, constraints and generalized brackets.

Degrees of freedom and Hamiltonian formalism for f(T) gravity

The existence of an extra degree of freedom (d.o.f.) in [Formula: see text] gravity has been recently proved by means of the Dirac formalism for constrained Hamiltonian systems. We will show a toy model displaying the essential feature of [Formula: see text] gravity, which is the pseudo-invariance of [Formula: see text] under a local symmetry, to understand the nature of the extra d.o.f.

Electron dynamics in strained graphene

This paper presents a theoretical description of the effects of strain induced by out-of-plane deformations on charge distributions and transport on graphene. A review of a continuum model for electrons using the Dirac formalism is complemented with elasticity theory to represent strain fields. The resulting model is cast in terms of scalar and pseudo-magnetic fields that control electron dynamics. Two distinct geometries, a bubble and a fold, are chosen to represent the most commonly observed deformations in experimental settings. It is shown that local charge accumulation regions appear in deformed areas, with a peculiar charge distribution that favors occupation of one sublattice only. This unique phenomenon that allows to distinguish each carbon atom in the unit cell, is the manifestation of a sublattice symmetry broken phase. For specific parameters, resonant states appear in localized charged regions, as shown by the emergence of discrete levels in band structure calculations. These findings are presented in terms of intuitive pictures that exploit analogies with confinement produced by square barriers. In addition, electron currents through strained regions are spatially separated into their valley components, making possible the manipulation of electrons with different valley indices. The degree of valley filtering (or polarization) for a specific system can be controlled by properly designing the strained area. The comparison between efficiencies of filters built with this type of geometries identifies extended deformations as better valley filters. A proposal for their experimental implementations as component of devices, and a discussion for potential observation of novel physics in strained structures are presented at the end of the paper.

Introduction to Fermionic Structures in C4 Space-Time

We explore several ways, in order to include fermionic structures naturally in a physical theory in C4. We begin with the standard Dirac formalism and we proceed by using Cartan's property of triality as a second option. Afterwards, we suggest a new approach (in a preliminary basis), by introducing an 1-linear form, as the "square root of the geometry" derived by the usual 2-linear forms (quadratic forms). Keeping this way, we introduce n-linear forms, in order to formulate a new geometric structure, which could be suitable for the formulation of a pure geometric unied theory.

Composite particles within the Faddeev–Jackiw framework: Nonequivalence between the Dirac and Faddeev–Jackiw formalisms

Some time ago, the Faddeev–Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables in the field theory context was reviewed. In the present work, the resulting formalism is applied to a classical nonrelativistic U(1) ×U(1) gauge field model that describes the electromagnetic interaction of composite particles in 2+1 dimensions. The model contains a Chern–Simons U(1) field and the electromagnetic field, and it uses either a composite boson system or a composite fermion one. The obtained results are compared with the ones corresponding to the implementation of the Dirac formalism to this model, concluding that the Faddeev–Jackiw and Dirac methods cannot be considered equivalent. A simplified version of the above model is analyzed in the same way, similar to the one used within the framework of condensed matter. In this case, it is observed that when the results obtained by the Faddeev–Jackiw and Dirac methods coincide, the first method is more economical than the second one. For both models, the composite fermion case is explicitly considered.