Symmetries of Maxwell’s Equations

Fushchich, W. I.; Nikitin, A. G.

doi:10.1007/978-94-009-3729-1

Cited by 127 publications

(225 citation statements)

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“…The Galilei transformations, along with the associate quantummechanical operators are [2]: -space translations: x i → x ′ i = x i + a i ; P i = −i∂ i -time translation: t → t ′ = t + a;…”

Section: The Galilei Group and The Lorentz Groupmentioning

confidence: 99%

Spin in Quantum Field Theory

Forte

2007

Modern Aspects of Spin Physics

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I introduce spin in field theory by emphasizing the close connection between quantum field theory and quantum mechanics. First, I show that the spin-statistics connection can be derived in quantum mechanics without relativity or field theory. Then, I discuss path integrals for spin without using spinors. Finally, I show how spin can be quantized in a path-integral approach, without introducing anticommuting variables.

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Section: The Galilei Group and The Lorentz Groupmentioning

confidence: 99%

Spin in Quantum Field Theory

Forte

2007

Modern Aspects of Spin Physics

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“…Instead of performing this straightforward but rather lengthy computation, it is sufficient to refer the literature. In 1958, Foldy encountered the problem for relativistic systems with various spins [4] (see also [30]). Let us follow the existing procedure by introducing a transformation 4 B = (8ω)…”

Section: Lorentz Invariancementioning

confidence: 99%

A positive-definite scalar product for free Proca particle

Jakubský

Smejkal

2006

Czech J Phys

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“…An equivalent (and more algorithmic) definition is the following one [10]. The operator Q is a symmetry operator of equation (11) if there is such an m-th order differential operator P that…”

Section: B Lie Symmetriesmentioning

confidence: 99%

“…Next, we make use of a well-known fact in the theory of high-order Lie symmetries of linear differential equations (see, e.g., [10]). Let…”

Section: Lemma 1 the Hamiltonianmentioning

confidence: 99%

The stationary KdV hierarchy and so(2,1) as a spectrum generating algebra

Doebner

Zhdanov

1999

Journal of Mathematical Physics

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The family F L of all potentials V (x) for which the Hamiltonian H = − d 2 dx 2 + V (x) in one space dimension possesses a high order Lie symmetry is determined. A sub-family F 2 SGA of F L , which contains a class of potentials allowing a realization of so(2, 1) as spectrum generating algebra of H through differential operators of finite order, is identified. Furthermore and surprisingly, the families F 2 SGA and F L are shown to be related to the stationary KdV hierarchy. Hence, the 'harmless' Hamiltonian H connects different mathematical objects, high order Lie symmetry, realization of so(2, 1)-spectrum generating algebra and families of nonlinear differential equations. We describe in a physical context the interplay between these objects.

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Symmetries of Maxwell’s Equations

Cited by 127 publications

References 0 publications

Spin in Quantum Field Theory

Spin in Quantum Field Theory

A positive-definite scalar product for free Proca particle

The stationary KdV hierarchy and so(2,1) as a spectrum generating algebra

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