Symplectic Field Theory of the Galilean Covariant Scalar and Spinor Representations

Petronilo, G. X. A.; Ulhoa, S. C.; Santana, A. E.

doi:10.15407/ujpe64.8.719

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…The Galilean covariant tensor formalism in phase space using the approach of symplectic quantum mechanics has been developed recently [16,17]. The path integral formalism of Galilean covariance in phase space is developed to consider the calculations of TFD.…”

Section: Introductionmentioning

confidence: 99%

Size-effect at finite temperature in a quark-antiquark effective model in phase space

Petronilo,

Amorim,

Ulhoa

et al. 2021

Preprint

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A quark-antiquark effective model is studied in a toroidal topology at finite temperature. The model is described by a Schrödinger equation with linear potential which is embedded in a torus. The following aspects are analysed: (i) the nonclassicality structure using the Wigner function formalism; (ii) finite temperature and size-effects are studied by a generalization of Thermofield Dynamics written in phase space; (iii) in order to include the spin of the quark, Pauli-like Schrödinger equation is used; (iv) analysis of the size-effect is considered to observe the fluctuation in the ground state. The size effect goes to zero at zero, finite and high temperatures. The results emphasize that the spin is a central aspect for this quark-antiquark effective model.

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Section: Introductionmentioning

confidence: 99%

Size-effect at finite temperature in a quark-antiquark effective model in phase space

Petronilo,

Amorim,

Ulhoa

et al. 2021

Preprint

Self Cite

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show abstract

“…In similar cases, the Galilean covariance permits the breaking of spin degeneracy without the use of perturbation theory. One important but still little studied is the generalization of Galilean covariance to a quantum phase space [6]. This is one of our goals here.…”

Section: Introductionmentioning

confidence: 99%

“…We develop and expand preliminary results in the study of the Galilean covariance in phase space [6]. Specifically, we obtain the symplectic version of the Pauli-Schrödinger equation.…”

Section: Introductionmentioning

confidence: 99%

The Landau Problem and non-Classicality

Petronilo,

Ulhoa,

Araújo

et al. 2020

Preprint

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Exploring the concept of the extended Galilei group G. Representations for field theories in a symplectic manifold have been derived in association with the method of the Wigner function. The representation is written in the light-cone of a de Sitter space-time in five dimensions. A Hilbert space is constructed, endowed with a symplectic structure, which is used as a representation space for the Lie algebra of G. This representation gives rise to the spin-zero Schrödinger (Klein-Gordonlike) equation for the wave functions in phase space, such that the dependent variables have the content of position and linear momentum. This is a particular example of a conformal theory, such that the wave functions are associated with the Wigner function through the Moyal product. We construct the Pauli-Schrödinger (Dirac-like) equation in phase space in its explicitly covariant form. In addition, we analyze the gauge symmetry for spin 1/2 particles in phase space and show how implement the minimal coupling in this case. We applied to the problem of an electron in an external field, and we recovered the non-relativistic Landau Levels. Finally, we study the parameter of negativity associated with the non-classicality of the system.

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The Landau problem and nonclassicality

Petronilo

Ulhoa

Araújo

et al. 2020

Int. J. Mod. Phys. A

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Exploring the concept of the extended Galilei group [Formula: see text]. Representations for field theories in a symplectic manifold have been derived in association with the method of the Wigner function. The representation is written in the light-cone of a de Sitter space–time in five dimensions. A Hilbert space is constructed, endowed with a symplectic structure, which is used as a representation space for the Lie algebra of [Formula: see text]. This representation gives rise to the spin-0 Schrödinger (Klein–Gordon-like) equation for the wave functions in phase space, such that the dependent variables have the content of position and linear momentum. This is a particular example of a conformal theory, such that the wave functions are associated with the Wigner function through the Moyal product. We construct the Pauli–Schrödinger (Dirac-like) equation in phase space in its explicitly covariant form. In addition, we analyze the gauge symmetry for spin-1/2 particles in phase space and show how implement the minimal coupling in this case. We applied to the problem of an electron in an external field, and we recovered the nonrelativistic Landau levels. Finally, we study the parameter of negativity associated with the nonclassicality of the system.

show abstract

Symplectic Field Theory of the Galilean Covariant Scalar and Spinor Representations

Cited by 4 publications

References 12 publications

Size-effect at finite temperature in a quark-antiquark effective model in phase space

Size-effect at finite temperature in a quark-antiquark effective model in phase space

The Landau Problem and non-Classicality

The Landau problem and nonclassicality

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