Deformed Quantum Phase Spaces, Realizations, Star Products and Twists

Meljanac, Stjepan; Štrajn, Rina

doi:10.48550/arxiv.2112.12038

Cited by 5 publications

(7 citation statements)

References 109 publications

(184 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The scheme presented above has been very recently generalized (see [25]), where in particular it is generalized basic quantum phase space commutator (23).…”

Section: Yang = 4 Quantum Phase Spacesmentioning

confidence: 99%

See 1 more Smart Citation

Noncommutative spaces and superspaces from Snyder and Yang type models

Lukierski¹,

Woronowicz²

2022

Preprint

View full text Add to dashboard Cite

The relativistic = 4 Snyder model is formulated in terms of = 4 algebra (4, 1) generators, with noncommutative Lorentz-invariant Snyder quantum space-time provided by (4,1) (3,1) coset generators. Analogously, in relativistic = 4 Yang models the quantum-deformed relativistic phase space is described by the algebras of coset generators (5,1) (3,1) or (4,2) (3,1) . We extend these algebraic considerations by using respective superalgebras, which provide Lorentz-covariant quantum superspaces (SUSY Snyder model) as well as relativistic quantum phase super spaces (SUSY Yang model).

show abstract

“…The scheme presented above has been very recently generalized (see [25]), where in particular it is generalized basic quantum phase space commutator (23).…”

Section: Yang = 4 Quantum Phase Spacesmentioning

confidence: 99%

“…The relations above can be supplemented by = 3 version of relations ( 24)- (25). We see that the relations (68)-(69) depend on the quantum superspace coordinates (67) as well as the covariance symmetry generators (66).…”

mentioning

confidence: 96%

Noncommutative spaces and superspaces from Snyder and Yang type models

Lukierski¹,

Woronowicz²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Construction of such quadratic algebras can be performed using twist operators that besides the Lorentz generators M µν include dilation operators and more generally L µν = x µ p ν . One example of such twist is (see [42])…”

Section: Snyder Space With Symmetric Ordering and Without Weyl Realiz...mentioning

confidence: 99%

“…A class of deformed quantum phase spaces, i.e. a deformed Heisenberg algebra, is generated with NC coordinates xµ and commutative momenta p µ defined as (see for example [42])…”

Section: Introductionmentioning

confidence: 99%

Symmetric ordering and Weyl realizations for quantum Minkowski spaces

Meljanac¹,

Škoda²,

Krešić–Jurić³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Symmetric ordering and Weyl realizations for non commutative quantum Minkowski spaces are reviewed. Weyl realizations of Lie deformed spaces and corresponding star products, as well as twist corresponding to Weyl realization and coproduct of momenta are presented. Drinfeld twists understood in Hopf algebroid sense are also discussed. A few examples of corresponding Weyl realizations are given. We show that for the original Snyder space there exists symmetric ordering, but no Weyl realization. Quadratic deformations of Minkowski space are considered and it is demonstrated that symmetric ordering is deformed and a generalized Weyl realization can be defined.

show abstract

“…A subtle point arises when one tries to introduce interactions. Many proposals of QFT in κ-Minkowski and Snyder space have been done in the literature [35,[77][78][79][80][81][82][83][84][85], most of them relying on the defnition of an appropriate Moyal-Groenewold product (also called star-product) [86][87][88][89]. The latter encodes the nontrivial addition of momenta and, generally speaking, can be built in a case by case analysis.…”

Section: B An Action For Scalar Fieldsmentioning

confidence: 99%

Geometrize and conquer: the Klein-Gordon and Dirac equations in Doubly Special Relativity

Franchino-Viñas¹,

Relancio²

2022

Preprint

View full text Add to dashboard Cite

In this work we discuss the deformed relativistic wave equations, namely the Klein-Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum space, which should be seen as complementary to the more spread algebraic one. In this frame we are able to rederive well-known algebraic expressions, as well as to treat yet unresolved issues, to wit, the explicit relation between both equations, the discrete symmetries for Dirac particles, the fate of covariance, and the formal definition of a Hilbert space for the Klein-Gordon case.

show abstract

Deformed Quantum Phase Spaces, Realizations, Star Products and Twists

Cited by 5 publications

References 109 publications

Noncommutative spaces and superspaces from Snyder and Yang type models

Noncommutative spaces and superspaces from Snyder and Yang type models

Symmetric ordering and Weyl realizations for quantum Minkowski spaces

Geometrize and conquer: the Klein-Gordon and Dirac equations in Doubly Special Relativity

Contact Info

Product

Resources

About