Multipole Theory In Electromagnetism: Classical, Quantum, And Symmetry Aspects, With Applications (International Series of Monographs on Physics) (International Series of Monographs on Physics (128))

This book provides an introduction to the classical, quantum and symmetry aspects of multipole theory, demonstrating the successes of the theory and also its unphysical aspects. It presents a transformation theory, which removes these unphysical properties. The book will be of interest to physics students wishing to advance their knowledge of multipole theory, and also a useful reference work for molecular and optical physicists, theoretical chemists working on multipole effects, solid state physicists studying the effects of electromagnetic fields on condensed matter, engineers and applied mathematicians with interests in anisotrpoic materials. An interesting recent development has been the increasing use of computer calculations in applications of multipole theory. The book should assist computational physicists and chemists wishing to work in this area to acquire the necessary background in multipole theory. Preface CONTENTS 1 Classical multipole theory 1.1 Multipole expansion for the potential of a finite static charge distribution 1.2 Dependence of electric multipole moments on origin 1.3 Permanent and induced multipole moments 1.4 Force and torque in an external electrostatic field 1.5 Potential energy of a charge distribution in an electrostatic field 1.6 Multipole expansion for the vector potential of a finite distribution of steady current 1.7 Dependence of magnetic multipole moments on origin 1.8 Force and torque in an external magnetostatic field 1.9 Potential energy of a current distribution in a magnetostaic field 1.10 Multipole expansions for the dynamic scalar and vector potentials 1.11 The far- and near-zone limits 1.12 Macroscopic media 1.13 Maxwell's macroscopic equations: multipole forms for D and H 1.14 Discussion 1.15 Primitive moments versus traceless moments 1.15.1 A charge distribution 1.15.2 Macroscopic media References 2 Quantum theory of multipole moments and polarizabilities 2.1 Semi-classical quantum mechanics 2.2 Electrostatic perturbation 2.3 Buckingham's derivation of electrostatic multipole moments 2.4 Magnetostatic perturbation 2.5 Time-dependent fields: standard gauge 2.6 Time-dependent fields: the Barron-Gray gauge 2.7 Polarizabilities for harmonic plane wave fields 2.8 Absorption of radiation 2.9 Additional static magnetic polarizabilities 2.10 Symmetries 2.11 Macroscopic multipole moment and polarizability densities 2.12 Phenomenology of the wave–matter interaction References 3 Space and time properties 3.1 Coordinate transformations 3.2 Vectors 3.3 Cartesian tensors 3.4 Time reversal 3.5 The space and time nature of various tensors 3.6 Symmetry and property tensors 3.7 Origin dependence of polarizability tensors 3.8 A pictorial determination of symmetry conditions 3.9 Discussion References 4 Linear constitutive relations from multipole theory 4.1 Constitutive relations 4.2 Origin independence 4.3 Symmetries 4.4 The "Post constraint" 4.5 Comparison with direct multipole results 4.5.1 Electric dipole order 4.5.2 Electric quadrupole–magnetic dipole order 4.5.3 Electric octopole–magnetic quadrupole order 4.6 Discussion References 5 Transmission and scattering effects: direct multipole results 5.1 The wave equation 5.2 Intrinsic Faraday rotation in a ferromagnetic crystal 5.3 Natural optical activity 5.4 Time-odd linear birefringence in magnetic cubics 5.5 Optical properties in the Jones calculus 5.6 Gyrotropic birefringence 5.7 Linear birefringence in non-magnetic cubic crystals (Lorentz birefringence) 5.8 Intrinsic Faraday rotation in magnetic cubics 5.9 The Kerr effect in an ideal gas 5.10 Forward scattering theory of the Kerr effect 5.11 Birefringence induced in a gas by an electric field gradient: forward scattering theory 5.11.1 Forward scattering by a molecule 5.11.2 Induced moments 5.11.3 Forward scattering by a lamina 5.11.4 The electrostatic field 5.11.5 Radiated field for linearly polarized light 5.11.6 Field-gradient-induced birefringence 5.11.7 Comparison between theory and experiment 5.12 Birefringence induced in a gas by an electric field gradient: wave theory 5.13 Discussion References 6 Reflection effects: direct multipole results 6.1 Reflection and the reflection matrix 6.2 The principle of reciprocity 6.3 Equations of continuity 6.4 Matching conditions in multipole theory 6.5 The reflection matrix lor non-magnetic uniaxial and cubic crystals 6.6 Solutions of the wave equation 6.7 Reflection coefficients 6.8 Tests of translational and time-reversal invariance 6.9 Discussion References 7 Transformations of the response fields and the constitutive tensor 7.1 Gauge transformations of the 4-vector potential 7.2 "Gauge transformations" of response fields 7.3 Faraday transformations 7.4 Transformations of linear constitutive relations in multipole theory References 8 Applications of the gauge and Faraday transformations 8.1 Electric dipole order 8.2 Electric quadrupole–magnetic dipole order, non-magnetic medium 8.3 Electric quadrupole–magnetic dipole order, magnetic medium 8.4 Discussion References 9 Transmission and reflection effects: transformed multipole results 9.1 The wave equation and transmission 9.2 Reflection from non-magnetic uniaxial and cubic crystals 9.3 Explicit results for non-magnetic uniaxial crystals 9.4 Explicit results for non-magnetic cubic crystals 9.5 Tests of translational and time-reversal invariance 9.6 Reflection from antiferromagnetic Cr[sub(2)]O[sub(3)]: first configuration 9.7 Reflection from antiferromagnetic Cr[sub(2)]O[sub(3)]: second configuration 9.8 Comparison with experiment for Cr[sub(2)]O[sub(3)] 9.9 Uniqueness of fields 9.10 Summary References A: Transformations involving J B: Magnetostatic field C: Magnetostatic force D: Magnetostatic torque E: Integral transformations F: Origin dependence of a polarizability tensor G: Invariance of transformed tensors Glossary of symbols A B C D E F G H I J K L M N P Q R S T U V W X Y Z Index A B C D E F G H I J K L M N O P Q R S T U V W This book provides an introduction to the classical, quantum, and symmetry aspects of multipole theory, demonstrating the successes of the theory and also its unphysical aspects. It presents a transformation theory which removes these unphysical properties. The book will be of interest to physics students wishing to advance their knowledge of multipole theory, and also a useful reference work for molecular and optical physicists, theoretical chemists working on multipole effects, solid state physicists studying the effects of electromagnetic fields on condensed matter, engineers and applied mathematicians with interests in anisotropic materials. An interesting recent development has been the increasing use of computer calculations in applications of multipole theory. The book will assist computational physicists and chemists wishing to work in this area to acquire the necessary background in multipole theory. Multipole theory provides a powerful way of characterising the electromagnetic behaviour of a medium, be it microscopic or macroscopic. This text decribes the concept of multipole theory as well as its successes and failures in applications to transmission, scattering and reflection. Multipole theory provides a powerful way of characterising the electromagnetic behaviour of a medium, be it microscopic or macroscopic. This text describes the concept of multipole theory as well as its successes and failures in applications to transmission, scattering and reflection Printbegrænsninger: Der kan printes 1 kapitel eller op til 5% af teksten