R-matrix and covariant q-superoscillators for U<sub>q</sub>(gl(1 mod 1))

Wallet, Jean-Christophe

doi:10.1088/0305-4470/25/19/005

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…algebra generators in terms of creation and annihilation operators [71][72][73][74][75]. Then one can show that this Poisson subalgebra is also a Wick-Voros subalgebra, that is…”

Section: Jhep04(2013)115mentioning

confidence: 97%

Noncommutative field theories on $ \mathbb{R}_{\lambda}^3 $: towards UV/IR mixing freedom

Vitale

Wallet

2013

J. High Energ. Phys.

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Abstract:We consider the noncommutative space R 3 λ , a deformation of the algebra of functions on R 3 which yields a "foliation" of R 3 into fuzzy spheres. We first construct a natural matrix base adapted to R 3 λ . We then apply this general framework to the one-loop study of a two-parameter family of real-valued scalar noncommutative field theories with quartic polynomial interaction, which becomes a non-local matrix model when expressed in the above matrix base. The kinetic operator involves a part related to dynamics on the fuzzy sphere supplemented by a term reproducing radial dynamics. We then compute the planar and non-planar 1-loop contributions to the 2-point correlation function. We find that these diagrams are both finite in the matrix base. We find no singularity of IR type, which signals very likely the absence of UV/IR mixing. We also consider the case of a kinetic operator with only the radial part. We find that the resulting theory is finite to all orders in perturbation expansion.

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“…algebra generators in terms of creation and annihilation operators [71][72][73][74][75]. Then one can show that this Poisson subalgebra is also a Wick-Voros subalgebra, that is…”

Section: Jhep04(2013)115mentioning

confidence: 97%

Noncommutative field theories on $ \mathbb{R}_{\lambda}^3 $: towards UV/IR mixing freedom

Vitale

Wallet

2013

J. High Energ. Phys.

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“…(For the non-standard two-parameter deformations of GL(1=1) we refer to [12], [13], [14].) In the case of oneparametric deformation the superalgebra U q (gl(m=n)) in duality with GL q (m=n) and its quantum subsuperalgebra U q (sl(m=n)) were studied in, e.g., [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35]. However, there was not much study of the multiparameter deformations of U(gl(m=n)) and U(sl(m=n)) and their interrelations, namely, t w o-parameter deformations were obtained for m = n = 1 in [36], [5], [8], and multiparameter deformations of U(sl(m=n)) were obtained in [37], and of U(sl(m=1)) in [38].…”

Section: Introductionmentioning

confidence: 99%

Induced representations of the multiparameter Hopf Superalgebras U_uq(gl(m/n)) and U_uq(sl(m/n))

Dobrev

Tahri

1999

J. Phys. A: Math. Gen.

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We construct induced representations of the multiparameter Hopf superalgebras U uq (gl(m=n)) and U uq (sl(m=n)). The rst superalgebra we constructed earlier as the dual of the multiparameter quantum deformation of the supergroup GL(m=n). The second superalgebra is a Hopf subalgebra of the rst for a special choice of the parameters. The representations are labelled by m + n integer numbers, respectively m + n 1 complex numbers, and act in the space of formal power series of (m + n)(m + n 1)=2 noncommuting variables, of which mn are odd and the rest are even. These variables generate a q-deformation of a ag supermanifold of the supergroup GL(m=n), respectively SL(m=n).2

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R-matrix and q-covariant oscillators for

Leblanc

Wallet²

1993

Physics Letters B

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R-matrix and covariant q-superoscillators for U_q(gl(1 mod 1))

Cited by 4 publications

References 16 publications

Noncommutative field theories on $ \mathbb{R}_{\lambda}^3 $: towards UV/IR mixing freedom

Noncommutative field theories on $ \mathbb{R}_{\lambda}^3 $: towards UV/IR mixing freedom

Induced representations of the multiparameter Hopf Superalgebras U_uq(gl(m/n)) and U_uq(sl(m/n))

R-matrix and q-covariant oscillators for

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R-matrix and covariant q-superoscillators for Uq(gl(1 mod 1))

Cited by 4 publications

References 16 publications

Noncommutative field theories on $ \mathbb{R}_{\lambda}^3 $: towards UV/IR mixing freedom

Noncommutative field theories on $ \mathbb{R}_{\lambda}^3 $: towards UV/IR mixing freedom

Induced representations of the multiparameter Hopf Superalgebras Uuq(gl(m/n)) and Uuq(sl(m/n))

R-matrix and q-covariant oscillators for

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R-matrix and covariant q-superoscillators for U_q(gl(1 mod 1))

Induced representations of the multiparameter Hopf Superalgebras U_uq(gl(m/n)) and U_uq(sl(m/n))