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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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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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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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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 |
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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[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.; Latini, E.; Lledo, M.A.; Nadal, F.A. |
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Title |
The Segre embedding of the quantum conformal superspace |
Type |
Journal Article |
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Year |
2018 |
Publication |
Advances in Theoretical and Mathematical Physics |
Abbreviated Journal |
Adv. Theor. Math. Phys. |
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Volume |
22 |
Issue |
8 |
Pages |
1939-2000 |
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Abstract |
In this paper we study the quantum deformation of the superflag Fl(2 vertical bar 0, 2 vertical bar 1, 4 vertical bar 1), and its big cell, describing the complex conformal and Minkowski superspaces respectively. In particular, we realize their projective embedding via a generalization to the super world of the Segre map and we use it to construct a quantum deformation of the super line bundle realizing this embedding. This strategy allows us to obtain a description of the quantum coordinate superring of the superflag that is then naturally equipped with a coaction of the quantum complex conformal supergroup SLq (4 vertical bar 1). |
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[Fioresi, R.; Latini, E.] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy, Email: rita.fioresi@UniBo.it; |
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Int Press Boston, Inc |
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English |
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ISSN |
1095-0761 |
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Notes |
WOS:000475480800004 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4102 |
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Author |
Lledo, M.A. |
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Title |
Superfields, Nilpotent Superfields and Superschemes dagger |
Type |
Journal Article |
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Year |
2020 |
Publication |
Symmetry-Basel |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
12 |
Issue |
6 |
Pages |
1024 - 32pp |
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Keywords |
supergeometry; superfields; quantum field theory |
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Abstract |
We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. We study the non-trivial relation of scalar superfields with the defining sheaf of the supermanifold of super spacetime. We also investigate in the present work some constraints that are imposed on the superfields, which allow for non-trivial solutions. They give rise to superschemes that, generically, are not regular, that is they do not define a standard supermanifold. |
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Address |
[Antonia Lledo, Maria] Univ Valencia, Dept Fis Teor, C Dr Moliner 50, E-46100 Burjassot, Valencia, Spain, Email: maria.lledo@ific.uv.es |
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Mdpi |
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English |
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Notes |
WOS:000550827300001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
4468 |
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