On scalar electromagnetism in phase space

Amorim, R. G. G.; Filho, Joilson Sodré; Santos, A. F.; Ulhoa, S. C.

doi:10.1142/s0217751x18501312

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…The product of two operators, AB, both defined in H , is associated to a Weyl product or star product of their phase space correspondents, i.e. [61][62][63][64][65][66][67][68][69],…”

Section: Introductionmentioning

confidence: 99%

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Luz

Petronilo

et al. 2022

Advances in High Energy Physics

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In this paper, we study within the structure of Symplectic Quantum Mechanics a bidimensional nonrelativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which consists of Coulomb-type plus linear potentials. First, we solve the Schrödinger equation in the phase space with the linear potential. The solution (ground state) is obtained and analyzed by means of the Wigner function related to Airy function for the c c ¯ meson. In the second case, to treat the Schrödinger-like equation in the phase space, a procedure based on the Bohlin transformation is presented and applied to the Cornell potential. In this case, the system is separated into two parts, one analogous to the oscillator and the other we treat using perturbation method. Then, we quantized the Hamiltonian with the aid of stars operators in the phase space representation so that we can determine through the algebraic method the eigenfunctions of the undisturbed Hamiltonian (oscillator solution), and the other part of the Hamiltonian was the perturbation method. The eigenfunctions found (undisturbed plus disturbed) are associated with the Wigner function via Weyl product using the representation theory of Galilei group in the phase space. The Wigner function is analyzed, and the nonclassicality of ground state and first excited state is studied by the nonclassicality indicator or negativity parameter of the Wigner function for this system. In some aspects, we observe that the Wigner function offers an easier way to visualize the nonclassic nature of meson system than the wavefunction does phase space.

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“…The product of two operators, AB, both defined in H , is associated to a Weyl product or star product of their phase space correspondents, i.e. [61][62][63][64][65][66][67][68][69],…”

Section: Introductionmentioning

confidence: 99%

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Luz

Petronilo

et al. 2022

Advances in High Energy Physics

View full text Add to dashboard Cite

show abstract

“…The product of two operators, AB, both defined in H, is associated to a Weyl product or star-product of their phase space correspondents, i.e. [41][42][43][44][45][46][47][48][49],…”

Section: Introductionmentioning

confidence: 99%

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Luz¹,

R.²,

Petronilo³

et al. 2021

Preprint

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In this paper, we explore a bi-dimensional nonrelativistic strong interaction system that represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which it has Coulombian and linear terms. For this purpose, we solve the Schrödinger equation in the phase space with the linear potential. The eigenfunction found is associated with the Wigner function via Weyl product using the representation theory of Galilei group in the phase space. We find that the Wigner function offers an easier way to visualize the properties of cc, bb, bc mesons systems than the wavefunction does.

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Symplectic representation of the Ginzburg–Landau theory

Reis,

Petronilo,

Amorim

et al. 2024

Int. J. Mod. Phys. A

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In this work, the Ginzburg–Landau theory is represented on a symplectic manifold with a phase space content. The order parameter is defined by a quasi-probability amplitude, which gives rise to a quasi-probability distribution function, i.e. a Wigner-type function. The starting point is the thermal group representation of Euclidean symmetries and gauge symmetry. Well-known basic results on the behavior of a superconductor are re-derived, providing the consistency of representation. The critical superconducting current density is determined and its usual behavior is inferred. The negativity factor associated with the quasi-distribution function is analyzed, providing information about the nonclassicality nature of the superconductor state in the region closest to the edge of the superconducting material.

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On scalar electromagnetism in phase space

Cited by 3 publications

References 21 publications

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Symplectic representation of the Ginzburg–Landau theory

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