Absence of the holographic principle in noncommutative Chern-Simons theory

Pinzul, A.; Stern, A.

doi:10.1088/1126-6708/2001/11/023

Cited by 28 publications

(52 citation statements)

References 13 publications

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“…From a more general point of view the results of this paper provide a first approach to the problem of solving star-equations with boundaries. This is a difficult but important problem as such equations are known to play a key part in several fields of research ranging from standard topics in quantum mechanics to some important developments in M-theory [26]. …”

Section: Discussionmentioning

confidence: 99%

“…These are much more realistic models and moreover they entail a discretization of observables' spectra, which is one of the main features of quantum mechanics. They appear in virtually all branches of physics, ranging from quantum mechanics to general relativity, open strings and Dbranes, where the non-commutative *-product and the Moyal bracket also find several applications [16,25,26]. In standard operator quantum mechanics some famous examples of boundary value problems include the Kondo problem [27], quantum Hall liquids with constriction [28] and the Callan-Rubakov model [29].…”

Section: Introductionmentioning

confidence: 99%

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Wigner functions with boundaries

Dias

Prata

2002

Journal of Mathematical Physics

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We consider the general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the "stargenvalue" equation and to the time evolution equation. These corrections can be cast in the form of a boundary potential contributing to the total Hamiltonian which together with a subsidiary boundary condition is responsible for the discretization of the energy levels. We show that a completely analogous formulation (in terms of boundary potentials) is also possible in standard operator quantum mechanics and that the Wigner and the operator formulations are also in one-to-one correspondence in the confined case. In particular, we extend Baker's converse construction to bounded systems. Finally, we elaborate on the applications of the formalism to the subject of Wigner trajectories, namely in the context of collision processes and quantum systems displaying chaotic behavior in the classical limit.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wigner functions with boundaries

Dias

Prata

2002

Journal of Mathematical Physics

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“…[32], Eqn. (4.16)) defined using the projection P N (see (3.2)) |z, N = P N |z ||P N |z || which, for the harmonic oscillator example, (3.1), becomes…”

Section: Coherent States In H Nmentioning

confidence: 99%

Exact operator bosonization of finite number of fermions in one space dimension

Dhar¹,

Mandal²,

Suryanarayana³

2006

J. High Energy Phys.

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Abstract:We derive an exact operator bosonization of a finite number of fermions in one space dimension. The fermions can be interacting or noninteracting and can have an arbitrary hamiltonian, as long as there is a countable basis of states in the Hilbert space. In the bosonized theory the finiteness of the number of fermions appears as an ultraviolet cut-off. We discuss implications of this for the bosonized theory. We also discuss applications of our bosonization to one-dimensional fermion systems dual to (sectors of) string theory such as LLM geometries and c=1 matrix model.

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“…[9] It was found that for these systems the question of taking the commutative limit and recovering systems with boundaries and edge states is subtle. [10] Recent progress has been made in [11] and [12]. The approach taken here may also be adapted in this direction.…”

Section: Introductionmentioning

confidence: 99%

Edge States from Defects on the Noncommutative Plane

Pinzul

Stern

2003

Mod. Phys. Lett. A

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We illustrate how boundary states are recovered when going from a noncommutative manifold to a commutative one with a boundary. Our example is the noncommutative plane with a defect, whose commutative limit was found to be a punctured plane -so here the boundary is one point. Defects were introduced by removing states from the standard harmonic oscillator Hilbert space. For Chern-Simons theory, the defect acts as a source, which was found to be associated with a nonlinear deformation of the w ∞ algebra. The undeformed w ∞ algebra is recovered in the commutative limit, and here we show that its spatial support is in a tiny region near the puncture. * Talk presented by second author at the conference "Space-time and Fundamental Interactions: Quantum Aspects" in honor of A.P. Balachandran's 65th birthday, Vietri sul Mare, Salerno, Italy 26th

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Absence of the holographic principle in noncommutative Chern-Simons theory

Cited by 28 publications

References 13 publications

Wigner functions with boundaries

Wigner functions with boundaries

Exact operator bosonization of finite number of fermions in one space dimension

Edge States from Defects on the Noncommutative Plane

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