2019
DOI: 10.1007/jhep07(2019)028
|View full text |Cite
|
Sign up to set email alerts
|

A fuzzy bipolar celestial sphere

Abstract: We introduce a non-commutative deformation of the algebra of bipolar spherical harmonics supporting the action of the full Lorentz algebra. Our construction is close in spirit to the one of the non-commutative spherical harmonics associated to the fuzzy sphere and, as such, it leads to a maximal value of the angular momentum. We derive the action of Lorentz boost generators on such non-commutative spherical harmonics and show that it is compatible with the existence of a maximal angular momentum.

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

0
10
0

Year Published

2020
2020
2024
2024

Publication Types

Select...
4
1

Relationship

0
5

Authors

Journals

citations
Cited by 6 publications
(10 citation statements)
references
References 36 publications
0
10
0
Order By: Relevance
“…Concerning bialgebra duals also the case of W 1 is better understood. All bialgebra structures are triangular and fully classified by means of the following Jordanian rmatrices: 16 r n = l 0 ∧ l n . The dual family of Lie algebra brackets in W • 1 reads now [56,58] [ε 0 , ε m ] n = (m − 2n)ε m−i , for m = 0 (B.8)…”
Section: Jhep02(2021)084mentioning
confidence: 99%
See 1 more Smart Citation
“…Concerning bialgebra duals also the case of W 1 is better understood. All bialgebra structures are triangular and fully classified by means of the following Jordanian rmatrices: 16 r n = l 0 ∧ l n . The dual family of Lie algebra brackets in W • 1 reads now [56,58] [ε 0 , ε m ] n = (m − 2n)ε m−i , for m = 0 (B.8)…”
Section: Jhep02(2021)084mentioning
confidence: 99%
“…In the recent paper [15] we constructed the κ-deformation of the BMS algebra (quantum deformations of BMS algebra were also considered in [16]) B 4 proposed by Barnich and Troessaert [5], which in addition to the infinitely many supertranslations contains an infinite number of superrotations, generalizing the Lorentz sector of the original BMS algebra B 4 BMS . The interest in such a deformation is at least threefold.…”
Section: Introductionmentioning
confidence: 99%
“…where π Λ is the N -dimensional unitary irreducible representation of U so (3). The latter is characterized by the condition π Λ (C) = Λ(Λ + 1), where C = E a E −a is the Casimir (sum over a ∈ {+, 0, −}), and E a make up the Cartan-Weyl basis E a of so (3).…”
Section: Diagonalization Of Toeplitz Tridiagonal Matricesmentioning
confidence: 99%
“…where π Λ is the N -dimensional unitary irreducible representation of U so (3). The latter is characterized by the condition π Λ (C) = Λ(Λ + 1), where C = E a E −a is the Casimir (sum over a ∈ {+, 0, −}), and E a make up the Cartan-Weyl basis E a of so (3). A set of generators of A Λ alternative to {x + , x − } is therefore {E + , E − } in the π Λ -representation, see [12] for details.…”
Section: Diagonalization Of Toeplitz Tridiagonal Matricesmentioning
confidence: 99%
See 1 more Smart Citation