Consequences of gauge invariance for fractionally charged quasi-particles (original) (raw)
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2019
We present here a theory of fractional electro-magnetism which is capable of describing phenomenon as disparate as the non-locality of the Pippard kernel in superconductivity and anomalous dimensions for conserved currents in holographic dilatonic models. The starting point for our analysis is the observation that the standard current conservation equations remain unchanged if any differential operator that commutes with the total exterior derivative multiplies the current. Such an operator, effectively changing the dimension of the current, increases the allowable gauge transformations in electromagnetism and is at the heart of N\"other's second theorem. Here we develop a consistent theory of electromagnetism that exploits this hidden redundancy in which the standard gauge symmetry in electromagnetism is modified by the rotationally invariant operator, the fractional Laplacian. We show that the resultant theories all allow for anomalous (non-traditional) scaling dimensions...
Localization of Fractionally Charged Quasi-Particles
Science, 2004
An outstanding question pertaining to the microscopic properties of the fractional quantum Hall effect is understanding the nature of the particles that participate in the localization but that do not contribute to electronic transport. By using a scanning single electron transistor, we imaged the individual localized states in the fractional quantum Hall regime and determined the charge of the localizing particles. Highlighting the symmetry between filling factors 1/3 and 2/3, our measurements show that quasi-particles with fractional charge e* = e /3 localize in space to submicrometer dimensions, where e is the electron charge.
Topological screening and interference of fractionally charged quasi-particles
Interference of fractionally charged quasi-particles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem, observables of an electronic system are invariant under adiabatic insertion of a quantum of singular flux. We resolve this seeming paradox by considering a microscopic model of an electronic Mach-Zehnder interferometer made from a quantum Hall liquid at filling factor 1/m. An approximate ground state of such an interferometer is described by a Laughlin type wave function, and low-energy excitations are incompressible deformations of this state. We construct a low-energy effective theory by projecting the state space of the liquid onto the space of such incompressible deformations and show that the theory of the quantum Hall edge so obtained is a generalization of a chiral conformal field theory. Amplitudes of quasi-particle tunneling in this theory are found to be insensitive to the magnetic fl...
Figshare.com, 2023
Inspired by the Fock-Ivanenko coefficients, we take advantage of a fractional gauge covariant derivative that bestows gauge invariance only up to first order in g (the gauge coupling) on the fractional QED (FQED) Lagrangian. As a result, we obtained several fractional wave equations; notably, the fractional ghost-we also show that this result can be ascertained by means of a nilpotent charge operator-, electromagnetic four-potential, and Weyl wave equations, after a modification of the QED-Lagrangian (a ghost sector is added to the Lagrangian). Furthermore, we show that the BRST fractional Lagrangian density does not succumb to the canonical Becchi-Rouet-Stora-Tyutin (BRST) transformations. But it does in the case of the ghost scaling symmetry transformations, in spite of the fractional treatment imposed on the Lagrangian. However, it turns out that these residual symmetries are dependent on the choice of fractional operator. In winding up, we consider additional wave equations for free gauge bosons and we explore the concept of Zitterbewegung-a fractional analog.