CURRENT OPERATORS IN THE LOWEST LANDAU LEVEL

1993 ◽  
Vol 07 (26) ◽  
pp. 4389-4401 ◽  
Author(s):  
JUAN MARTÍNEZ ◽  
MICHAEL STONE
Keyword(s):  
Landau Level ◽  
Current Operator ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Lowest Landau Level ◽  
Definition Of

We use Noether’s theorem to generate a consistent definition of the current operator for electrons restricted to the lowest Landau level. We exhibit the connection between this current and the Moyal bracket, or W∞, algebra, and use it to derive the edge-charge algebra for the ν=1/(2n+1) FQHE states.

scholarly journals About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof

2019 ◽  
Vol 22 (4) ◽  
pp. 871-898 ◽  
Author(s):  
Jacky Cresson ◽  
Anna Szafrańska
Keyword(s):  
Local Group ◽  
Type Theorem ◽  
Classical Case ◽  
Alternative Proof ◽  
Lagrangian Systems ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Definition Of ◽  
Variational Symmetries ◽  
Discrete Setting

Abstract Recently, the fractional Noether’s theorem derived by G. Frederico and D.F.M. Torres in [10] was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see [7]) using a counterexample and doubts are stated about the validity of other Noether’s type Theorem, in particular ([9], Theorem 32). However, the counterexample does not explain why and where the proof given in [10] does not work. In this paper, we make a detailed analysis of the proof proposed by G. Frederico and D.F.M. Torres in [9] which is based on a fractional generalization of a method proposed by J. Jost and X.Li-Jost in the classical case. This method is also used in [10]. We first detail this method and then its fractional version. Several points leading to difficulties are put in evidence, in particular the definition of variational symmetries and some properties of local group of transformations in the fractional case. These difficulties arise in several generalization of the Jost’s method, in particular in the discrete setting. We then derive a fractional Noether’s Theorem following this strategy, correcting the initial statement of Frederico and Torres in [9] and obtaining an alternative proof of the main result of Atanackovic and al. [3].

SUPERFIELDS AND CANONICAL METHODS IN SUPERSPACE

1986 ◽  
Vol 01 (04) ◽  
pp. 293-302 ◽  
Author(s):  
J.A. DE AZCÁRRAGA ◽  
J. LUKIERSKI ◽  
P. VINDEL
Keyword(s):  
Quantum Mechanics ◽  
Evolution Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Noether’S Theorem ◽  
Equal Time ◽  
Heisenberg Picture ◽  
Noether's Theorem ◽  
Time Limits ◽  
Definition Of

We consider the “supersymmetric roots” of the Heisenberg evolution equation as describing the dynamics of superfields in superspace. We investigate the superfield commutators and their equal time limits and exhibit their noncanonical character even for free superfields. For simplicity, we concentrate on the D=1 case, i.e., the superfield formulation of supersymmetric quantum mechanics in the Heisenberg picture and, as a soluble example, the supersymmetric oscillator. Finally, we express Noether’s theorem in superspace and give the definition of the global conserved supercharges.

CURRENTS IN THE LOWEST LANDAU LEVEL FIELD THEORY WITH e–e INTERACTIONS

1994 ◽  
Vol 08 (06) ◽  
pp. 777-788 ◽  
Author(s):  
R. RAJARAMAN
Keyword(s):  
Field Theory ◽  
Electric Current ◽  
Landau Level ◽  
External Force ◽  
Particle Interaction ◽  
Lagrangian Formulation ◽  
Field Equations ◽  
Noether’S Theorem ◽  
Lowest Landau Level ◽  
Nonlocal Field

We obtain expressions for the electric current in the Lowest Landau Level field theory in the presence of a general (external as well as inter-particle) interaction. This is done in the constrained Lagrangian formulation and is an extension of results obtained by Martinez and Stone for the external force case. However, we work directly with nonlocal field equations rather than convert the Lagrangian into a local one and use Noether's theorem.

scholarly journals LANDAU LEVEL MIXING AND SOLENOIDAL TERMS IN LOWEST LANDAU LEVEL CURRENTS

1994 ◽  
Vol 08 (17) ◽  
pp. 1065-1073 ◽  
Author(s):  
R. RAJARAMAN ◽  
S. L. SONDHI
Keyword(s):  
Landau Level ◽  
High Field ◽  
Electron System ◽  
Current Operator ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Field Limit ◽  
Lowest Landau Level ◽  
Dimensional Electron System ◽  
Landau Level Mixing

We calculate the lowest Landau level (LLL) current by working in the full Hilbert space of a two-dimensional electron system in a magnetic field and keeping all the nonvanishing terms in the high field limit. The answer i) is not represented by a simple LLL operator and ii) differs from the current operator, recently derived by Martinez and Stone in a field theoretic LLL formalism, by solenoidal terms. Though that is consistent with the inevitable ambiguities of their Noether construction, we argue that the correct answer cannot arise naturally in the LLL formalism.

scholarly journals EFFECTIVE INTERACTIONS OF PLANAR FERMIONS IN A STRONG MAGNETIC FIELD — THE EFFECT OF LANDAU LEVEL MIXING

1994 ◽  
Vol 08 (11) ◽  
pp. 687-698 ◽  
Author(s):  
RASHMI RAY ◽  
GIL GAT
Keyword(s):  
Landau Level ◽  
Current Operator ◽  
Finite Sample ◽  
Interparticle Interactions ◽  
Effective Interactions ◽  
Electromagnetic Interactions ◽  
Lowest Landau Level ◽  
Edge Current ◽  
Long Range Interactions ◽  
Landau Level Mixing

We obtain expressions for the current operator in the lowest Landau level (L.L.L.) field theory, where higher Landau level mixing due to various external and interparticle interactions is systematically taken into account. We consider the current operators in the presence of electromagnetic interactions, both Coulomb and time-dependent, as well as local four-Fermi interactions. The importance of Landau level mixing for long range interactions is especially emphasized. We also calculate the edge current for a finite sample.

scholarly journals Restoration of the symmetries broken by reversible growth in hyperelastic bodies

2003 ◽  
pp. 311-331 ◽  
Author(s):  
Alfio Grillo ◽  
Salvatore Federico ◽  
Gaetano Giaquinta ◽  
Walter Herzog ◽  
Rosa La
Keyword(s):  
The Body ◽  
Broken Symmetry ◽  
Reference Configuration ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Broken Symmetries ◽  
Elastic Bodies ◽  
Theoretical Investigations ◽  
Hyper Elastic ◽  
Definition Of

In this paper, we interpret the development of material in homogeneities in continuum, hyper elastic bodies in the presence of reversible growth in terms of broken symmetries [1]. By applying Noether's Theorem [1, 2, 3, 4], we find a set of equations yielding the fields necessary to compensate for the broken symmetry. As growth occurs, these fields provide for an instantaneously updated reference configuration of the body, and are responsible for the dynamical restoring of the body symmetries. In addition, we propose to use these compensating fields in order to generalize the definition of the transplant operator given in [5,6]. This work has been motivated by the current theoretical investigations on the biomechanical aspects of growth in particular cartilage.

Introduction

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Conservation Laws ◽  
Lagrangian Mechanics ◽  
General Introduction ◽  
Noether’S Theorem ◽  
Noether's Theorem

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is included.

scholarly journals Stochastic fractal and Noether's theorem

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Rakibur Rahman ◽  
Fahima Nowrin ◽  
M. Shahnoor Rahman ◽  
Jonathan A. D. Wattis ◽  
Md. Kamrul Hassan
Keyword(s):  
Noether’S Theorem ◽  
Noether's Theorem
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