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A classification of quantum Hall fluids
In this paper, the key ideas of characterizing universality classes of dissipationfree (incompressible) quantum Hall fluids by mathematical objects called quantum Hall lattices are reviewed. Many
Gauge invariance and current algebra in nonrelativistic many body theory
The main purpose of this paper is to further our theoretical understanding of the fractional quantum Hall effect, in particular of spin effects, in two-dimensional incompressible electron fluids
Boundary conditions for quantum mechanics on cones and fields around cosmic strings
We study the options for boundary conditions at the conical singularity for quantum mechanics on a two-dimensional cone with deficit angle ≦ 2π and for classical and quantum scalar fields propagating
The Fractional Quantum Hall Effect, Chern-Simons Theory, and Integral Lattices
Chern-Simons theory has come to play an important role in three-dimensional topology because of its connections with Ray-Singer analytic torsion [47], the Gauss linking number [25], [14], [57], the
U(1)×SU(2)-gauge invariance of non-relativistic quantum mechanics, and generalized Hall effects
We show that the non-relativistic quantum mechanics of particles with spin coupled to an electromagnetic field has a naturalU(1)×SU(2) gauge invariance. Ward identities reflecting this gauge
Incompressible Quantum Fluids, Gauge-Invariance, and Current Algebra
This rather long paper is a tale of non-relativistic quantum theory summarizing research that has been conducted during the last one and a half years, and the main results of which have been sketched
Quantum Theory of Large Systems of Non-Relativistic Matter
1. Introduction 2. The Pauli Equation and its Symmetries {2.1} Gauge-Invariant Form of the Pauli Equation {2.2} Aharonov-Bohm Effect {2.3} Aharonov-Casher Effect 3. Gauge Invariance in
Probability theory and inference: how to draw consistent conclusions from incomplete information
Probability theory seen as logic goes much beyond the so-called frequentists' schools of probability theory, as it is based on more fundamental assumptions (desiderata) and is far more flexible in its applications, as explained in this paper.