scholarly journals The deformation quantization of certain super-Poisson brackets and BRST cohomology

2000 ◽  
pp. 45-68 ◽  
Author(s):  
Martin Bordemann
Keyword(s):  
Deformation Quantization ◽  
Poisson Brackets ◽  
Brst Cohomology

scholarly journals BRST Cohomology and Phase Space Reduction in Deformation Quantization

2000 ◽  
Vol 210 (1) ◽  
pp. 107-144 ◽  
Author(s):  
Martin Bordemann ◽  
Hans-Christian Herbig ◽  
Stefan Waldmann
Keyword(s):  
Phase Space ◽  
Deformation Quantization ◽  
Space Reduction ◽  
Brst Cohomology ◽  
Phase Space Reduction

scholarly journals DEFORMATION QUANTIZATION OF CERTAIN NONLINEAR POISSON STRUCTURES

1998 ◽  
Vol 09 (05) ◽  
pp. 599-621 ◽  
Author(s):  
BYUNG-JAY KAHNG
Keyword(s):  
Poisson Bracket ◽  
Lie Algebra ◽  
Deformation Quantization ◽  
Dual Space ◽  
Poisson Brackets ◽  
Poisson Structures ◽  
Central Extensions ◽  
C Algebras ◽  
Lie Bracket ◽  
Compact Quantum Groups

As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain nonlinear Poisson brackets which are "cocycle perturbations" of the linear Poisson bracket. We show that these special Poisson brackets are equivalent to Poisson brackets of central extension type, which resemble the central extensions of an ordinary Lie bracket via Lie algebra cocycles. We are able to formulate (strict) deformation quantizations of these Poisson brackets by means of twisted group C*-algebras. We also indicate that these deformation quantizations can be used to construct some specific non-compact quantum groups.

scholarly journals N=2 SUPER-W-ALGEBRA IN THE HALF-TWISTED LANDAU-GINZBURG MODEL

1994 ◽  
Vol 09 (29) ◽  
pp. 5097-5120 ◽  
Author(s):  
KENJI MOHRI
Keyword(s):  
Cohomology Class ◽  
Minimal Model ◽  
Simple Formula ◽  
Poisson Brackets ◽  
Superconformal Symmetry ◽  
Miura Transformation ◽  
Coset Model ◽  
Brst Cohomology ◽  
Chiral Ring ◽  
Chiral Superfields

We investigate N=2 extended superconformal symmetry, using the half-twisted Landau-Ginzburg models. The first example is the D2n+2 type minimal model. It has been conjectured that this model has a spin n super-W-current. We check this by direct computations of the BRST cohomology class up to n=4. We observe that for n≤3 the super-W-currents generate the ring isomorphic to the chiral ring of the model with respect to the classical product. We thus conjecture that this isomorphism holds for any n. The next example is the CPn coset model. In this case we find a sort of Miura transformation which gives a simple formula for the super-W-currents of spin {1, 2, …, n} in terms of the chiral superfields. Explicit forms of the super-W-currents and their Poisson brackets are obtained for the CP2 and CP3 cases. We also conjecture that as far as the classical product is concerned, these super-W-currents generate the ring isomorphic to the chiral ring of the model, and this is checked for CP2 coset model.

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

Poisson Brackets & Angular Momentum

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Generating Functions ◽  
First Integrals ◽  
Lagrangian Mechanics ◽  
Poisson Brackets ◽  
Coordinate Transformations ◽  
Canonical Transformations ◽  
Gauge Transformations ◽  
The Third ◽  
Point Transformations ◽  
Canonical Coordinate

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.

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