Field Quantization

Greiner, Walter; Reinhardt, Joachim

doi:10.1007/978-3-642-61485-9

Cited by 477 publications

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“…All four polarization vectors form a complete and orthogonal system, and the TE and TM polarizations are complete in the subspace of physical states [16] g µν e µ σ e ν σ ′ = g σσ ′ ,…”

mentioning

confidence: 99%

Quantum electrodynamics near a dielectric half-space

Eberlein

Robaschik

2006

Phys. Rev. D

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confidence: 99%

Quantum electrodynamics near a dielectric half-space

Eberlein

Robaschik

2006

Phys. Rev. D

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“…[14], but taking into account that we are working in 2 + 1 dimensions, the electric field can be split in its transversal and longitudinal components in the plane of electron motion…”

Section: 4πmentioning

confidence: 99%

Alternative Derivation of the Mean-Field Equations for Composite Fermions

Manavella¹,

Repetto²

2015

JMP

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The Hamiltonian describing a composite fermion system is usually presented in a phenomenological way. By using a classical nonrelativistic U(1) × U(1) gauge field model for the electromagnetic interaction of electrons, we show how to obtain the mean-field Hamiltonian describing composite fermions in 2 + 1 dimensions. In order to achieve this goal, the Dirac Hamiltonian formalism for constrained systems is used. Furthermore, we compare these results with the ones corresponding to the inclusion of a topological mass term for the electromagnetic field in the Lagrangian. KeywordsQuantum Field Theory, Field Theories in Dimensions Other than Four, Chern-Simons Gauge Theory, Lagrangian and Hamiltonian Formalisms

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“…In the course of quantizing the free electromagnetic field in the Coulomb gauge with a plane wave basis [3,4] it is necessary to use the geometric relation in {x, y, z} space…”

Section: Appendix Bmentioning

confidence: 99%

“…The four components of the electromagnetic potential were promoted to operators and the commutation relations between them determined by analogy with those of the simple harmonic oscillator. The commutations relations are different in each gauge [3]. The quanta of the electromagnetic field are known as photons and the states that the operators act on are Fock states of photons (not necessarily plane waves) [5].…”

Section: Introductionmentioning

confidence: 99%

Quantisation of the free electromagnetic field implies quantisation of its angular momentum

Stewart

2011

Journal of Modern Optics

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It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the absence of electric and magnetic charge densities, these operators satisfy the canonical commutation relations for momentum and angular momentum. This confirms their validity as operators that can be used in quantum mechanical calculations of angular momentum. IntroductionThe free electromagnetic field was first quantized in a plane wave basis in the Coulomb gauge and later in the Lorenz gauge [1,2,3,4]. The four components of the electromagnetic potential were promoted to operators and the commutation relations between them determined by analogy with those of the simple harmonic oscillator. The commutations relations are different in each gauge [3]. The quanta of the electromagnetic field are known as photons and the states that the operators act on are Fock states of photons (not necessarily plane waves) [5]. By taking appropriate combinations of the derivatives of the potentials, Bohr and Rosenfeld [6] obtained the gauge-invariant equal time commutation relations between the field operators E(x,t) and B(y,t)

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Field Quantization

Cited by 477 publications

References 0 publications

Quantum electrodynamics near a dielectric half-space

Quantum electrodynamics near a dielectric half-space

Alternative Derivation of the Mean-Field Equations for Composite Fermions

Quantisation of the free electromagnetic field implies quantisation of its angular momentum

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