Galilei Group and Galilean Invariance

Lévy‐Leblond, Jean‐Marc

doi:10.1016/b978-0-12-455152-7.50011-2

Cited by 195 publications

(240 citation statements)

References 69 publications

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“…Apart from this, the two-parameter "exotic" central extension [5] is recovered. Our results extend those obtained in [4] to noncommutative CS gauge theory.…”

Section: Noncommutative Gauge Theorymentioning

confidence: 99%

Galilean noncommutative gauge theory: symmetries and vortices

Horváthy

Martina

Stichel³

2003

Nuclear Physics B

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Noncommutative Chern-Simons gauge theory coupled to nonrelativistic scalars or spinors is shown to admit the "exotic" two-parameter-centrally extended Galilean symmetry, realized in a unique way consistent with the Seiberg-Witten map. Nontopological spinor vortices and topological external-field vortices are constructed by reducing the problem to previously solved self-dual equations.hep-th/0306228

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“…Apart from this, the two-parameter "exotic" central extension [5] is recovered. Our results extend those obtained in [4] to noncommutative CS gauge theory.…”

Section: Noncommutative Gauge Theorymentioning

confidence: 99%

Galilean noncommutative gauge theory: symmetries and vortices

Horváthy

Martina

Stichel³

2003

Nuclear Physics B

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“…Since the wave function is a ray, it is a projective object, and as such we have to look at the action of the so-called projective representation of the Galilean group. Moreover, because the wave function evolution yields a unitary evolution, one has to restrict to the action of the projective and unitary representations of the Galilei group (Inönü and Wigner 1952), (Bargmann 1954), (Levy-Leblond 1963;1971). In general, to any invariance group in quantum mechanics should correspond a projective unitary representation of the group.…”

Section: The Physical Representation Of the Galilei Group And Classicmentioning

confidence: 99%

“…Because of this, ( , ) should be considered the only physical representation of the Galilean group in quantum mechanics. This representation can be interpreted as describing particles with mass , internal energy and spin (see again [Levy-Leblond 1971]). Writing the representation ( , ) in configuration space and in the Schrödinger picture, one has:…”

Section: The Physical Representation Of the Galilei Group And Classicmentioning

confidence: 99%

A New Argument for the Nomological Interpretation of the Wave Function: The Galilean Group and the Classical Limit of Nonrelativistic Quantum Mechanics

Allori

2017

International Studies in the Philosophy of Science

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In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non-Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function.

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“…Actually, in the light of present stage of quantum theory, it looks that the spin-orbit coupling is an effect of some approximations rather than a real interaction. Moreover, it should not be attributed to as a purely "relativistic" or "quantum" effect, but emerges also from theories based on Galilean group [4,5] and classical theory (like Thomas precession [6,7]). In this paper, however, we shall follow a traditional Lorentzian relativity and the quantum Dirac equation.…”

Section: Origin Of the Spin-orbit Interactionmentioning

confidence: 99%

Spin-Orbit Coupling for f-Electrons in a Crystalline Field

Lulek

1993

Acta Phys. Pol. A

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The notion of a spin-orbit interaction arises from consideration of dynamics of multielectron atoms, i.e. systems of N electrons in a spherical potential. This notion is essentially a single-particle one. We sketch its origin as a second-order correction when Dirac four-component wave equations for an electron in external electromagnetic fields are simplified to the two-component Pauli spinors. The constraints in spinorial degrees of freedom consist, roughly speaking, in neglecting the small component of the electron four-function. The spin-orbit interaction term serves to compensate effects of the small component. The crystalline field induces some deviations from spherical symmetry of an isolated atom, which yields some modifications of the spherical form of the spin-orbit interaction operator. These modifications can be described in terms of a number of tensor operators adapted to appropriate chains of subgroups of the spherical symmetry group. We present a classification of independent tensor operators and discuss the relevant parameters for f-ions.

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Galilei Group and Galilean Invariance

Cited by 195 publications

References 69 publications

Galilean noncommutative gauge theory: symmetries and vortices

Galilean noncommutative gauge theory: symmetries and vortices

A New Argument for the Nomological Interpretation of the Wave Function: The Galilean Group and the Classical Limit of Nonrelativistic Quantum Mechanics

Spin-Orbit Coupling for f-Electrons in a Crystalline Field

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