A representation of the Virasoro algebra via Wigner-Heisenberg algebraic technique to bosonic systems

Graca, E. L.; Carrion, H. L.; Rodrigues, R. de Lima

doi:10.1590/s0103-97332003000200034

Cited by 2 publications

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References 13 publications

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“…and one can see that the coupling constant defined in (17) must satisfy ( g > − 1 4 (1 ± c) 2 ). When the constant c vanishes the Casimir operator becomes L 2 = 1 16 (4g − 3), so that the ground state has the eigenvalue…”

Section: Conformal Symmetry In the Wigner-heisenberg Picturementioning

confidence: 99%

“…Since D and K do not commute with the Hamiltonian H, they do not generate symmetries in the usual sense of relating the degenerate states. Rather they can be used to relate states with different eigenvalues of H (17). It is possible to show in any quantum mechanics with operators obeying the SL(2,R) algebra (19), that if |χ is a state of energy E, then e ıαD is a state for the energy e 2α E. Thus, if there is a state of nonzero energy then the spectrum is continuous.…”

Section: Conformal Symmetry In the Wigner-heisenberg Picturementioning

confidence: 99%

“…Recently, the deformed Wigner-Heisenberg (WH) oscillator algebra has been investigated in the context of the generalized statistics (introduced in physics in the form of parastatistics as an extension of the Bose and Fermi statistics) [15,16]. On the other hand, the elements of the conformal group can be represented in terms of ladder operators of deformed quantum oscillators [17] and the WH-algebra has also been investigated in connection with noncommutative geometry [18,19].…”

Section: Introductionmentioning

confidence: 99%

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Superconformal Quantum Mechanics via Wigner–heisenberg Algebra

Carrion

Rodrigues

2010

Mod. Phys. Lett. A

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We show the natural relation between the Wigner Hamiltonian and the conformal Hamiltonian. It is presented a model in (super)conformal quantum mechanics with (super)conformal symmetry in the Wigner-Heisenberg algebra picture [x, p x ] = i(1 + cP) (P being the parity operator). In this context, the energy spectrum, the Casimir operator, creation and annihilation operators are defined. This superconformal Hamiltonian is similar to the super-Hamiltonian of the Calogero model and it is also an extension of the super-Hamiltonian for the Dirac Oscillator.

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Section: Conformal Symmetry In the Wigner-heisenberg Picturementioning

confidence: 99%

Section: Conformal Symmetry In the Wigner-heisenberg Picturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Superconformal Quantum Mechanics via Wigner–heisenberg Algebra

Carrion

Rodrigues

2010

Mod. Phys. Lett. A

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Lie algebras associated with the renormalized higher powers of white noise

Accardi¹,

Boukas²

2007

COSA

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We recall the recently established (cf.[1] and [2]) connection between the renormalized higher powers of white noise (RHPWN) * -Lie algebra and the Virasoro -Zamolodchikov-w∞ * -Lie algebra of conformal field theory (cf. [10]). Motivated by this connection, with the goal of investigating a possible connection with classical independent increments processes, we begin a systematic study of the sub- * -Lie algebras of the (1-mode) full oscillator algebra. This program has two additional motivations: (i) the full oscillator algebra is a fundamental object of mathematics and the structure of its subalgebras deserves deep investigation; (ii) the no-go theorems show that the current algebras over some Lie subalgebras of Lie algebras may have a Fock representation individually without this being true for the Lie algebra generated by them. The problem of classifying which sub-algebras of the full oscillator algebra have this property is open and a preliminary step towards its analysis is the classification of the "natural" sub-algebras of the full oscillator algebra.We construct two hierarchies of such sub-algebras, parametrized by the natural integers. One of these hierarchies begins with the Virasoro algebra. Another possibility to bypass the no-go theorems is to consider different renormalizations of the higher powers of white noise commutation relations. This approach is developed in Section 2, where we show with examples that some of them lead to known (i.e., first or second order) commutation relations. This fact is probably related with the gaussianization phenomenon discussed in [7].2000 Mathematics Subject Classification. Primary 60H40; Secondary 81S05. Key words and phrases. Higher powers of white noise functionals, Renormalization, Heisenberg commutation relations, Square of white noise commutation relations.

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A representation of the Virasoro algebra via Wigner-Heisenberg algebraic technique to bosonic systems

Abstract: Using the Wigner-Heisenberg algebra for bosonic systems in connection with oscillators we find a new representation for the Virasoro algebra.

Cited by 2 publications

References 13 publications

Superconformal Quantum Mechanics via Wigner–heisenberg Algebra

Superconformal Quantum Mechanics via Wigner–heisenberg Algebra

Lie algebras associated with the renormalized higher powers of white noise

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