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Author |
Fioresi, R.; Lledo, M.A. |
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Title |
Quantum Supertwistors |
Type |
Journal Article |
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Year |
2021 |
Publication |
Symmetry-Basel |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
13 |
Issue |
7 |
Pages |
1241 - 16pp |
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Keywords |
star products; superspace; non-commutative spacetime; quantum groups; quantum supergroups |
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Abstract |
In this paper, we give an explicit expression for a star product on the super-Minkowski space written in the supertwistor formalism. The big cell of the super-Grassmannian Gr(2|0,4|1) is identified with the chiral, super-Minkowski space. The super-Grassmannian is a homogeneous space under the action of the complexification SL(4|1) of SU(2,2|1), the superconformal group in dimension 4, signature (1,3), and supersymmetry N=1. The quantization is done by substituting the groups and homogeneous spaces by their quantum deformed counterparts. The calculations are done in Manin's formalism. When we restrict to the big cell, we can explicitly compute an expression for the super-star product in the Minkowski superspace associated to this deformation and the choice of a certain basis of monomials. |
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Address |
[Fioresi, Rita] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, I-40126 Bologna, Italy, Email: fioresi@dm.unibo.it; |
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Mdpi |
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English |
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Notes |
WOS:000677165600001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4909 |
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Author |
Fioresi, R.; Lledo, M.A.; Razzaq, J. |
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Title |
N=2 quantum chiral superfields and quantum super bundles |
Type |
Journal Article |
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Year |
2022 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
55 |
Issue |
38 |
Pages |
384012 - 19pp |
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Keywords |
supergeometry; supersymmetry; quantum groups; noncommutative geometry; Minkowski space |
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Abstract |
We give the superalgebra of N = 2 chiral (and antichiral) quantum superfields realized as a subalgebra of the quantum supergroup SL q (4|2). The multiplication law in the quantum supergroup induces a coaction on the set of chiral superfields. We also realize the quantum deformation of the chiral Minkowski superspace as a quantum principal bundle. |
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Address |
[Fioresi, R.] Univ Bologna, Fabit, Via San Donato 15, I-40126 Bologna, Italy, Email: rita.fioresi@unibo.it; |
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Publisher |
IOP Publishing Ltd |
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English |
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1751-8113 |
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Notes |
WOS:000849946700001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5351 |
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Author |
Aldana, M.; Lledo, M.A. |
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Title |
The Fuzzy Bit |
Type |
Journal Article |
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Year |
2023 |
Publication |
Symmetry-Basel |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
15 |
Issue |
12 |
Pages |
2103 - 25pp |
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Keywords |
fuzzy sets; quantum logic; multivalued logic; Quantum Mechanics |
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Abstract |
In this paper, the formulation of Quantum Mechanics in terms of fuzzy logic and fuzzy sets is explored. A result by Pykacz, which establishes a correspondence between (quantum) logics (lattices with certain properties) and certain families of fuzzy sets, is applied to the Birkhoff-von Neumann logic, the lattice of projectors of a Hilbert space. Three cases are considered: the qubit, two qubits entangled, and a qutrit 'nested' inside the two entangled qubits. The membership functions of the fuzzy sets are explicitly computed and all the connectives of the fuzzy sets are interpreted as operations with these particular membership functions. In this way, a complete picture of the standard quantum logic in terms of fuzzy sets is obtained for the systems considered. |
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Address |
[Aldana, Milagrosa] Univ Simon Bolivar, Dept Ciencias Tierra, Valle De Sartenejas 89000, Baruta, Venezuela, Email: maldana@usb.ve; |
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Mdpi |
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English |
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Notes |
WOS:001131238400001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5962 |
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