Dynamical Theory of Crystal Lattices

1955/10/01 by Max Born, Kun Huang, M. Lax · 10,577 citations
Computer Science · #Advanced Algebra and Logic #Classical mechanics #Crystal (programming language) #Physics #Quantum mechanics #Statistical physics #Theoretical physics

paper · doi:10.1119/1.1934059

published in American Journal of Physics 23(7), 474 (American Institute of Physics)

openalex publication_date 1955/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

At the time of its publication this classic text, co-written by the Nobel Laureate Max Born, represented the definitive account of the subject and in many ways it still does. The book begins with a general discussion of the statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. It then provides detailed discussions of long lattice waves, thermal properties, and optical properties.

Cited by

• A two-step strategy for designing stretch-dominated metamaterials simultaneously satisfying desired elastic tensor and bandgap
• Mechanics of carbon nanotubes
• Gibbs2: A new version of the quasiharmonic model code. II. Models for solid-state thermodynamics, features and implementation
• A promising all-inorganic double perovskite Rb2TiBr6 for photovoltaic applications: Insight from first-principles calculations
• Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems
• Electron-Phonon Interaction and Anisotropic Mobility in Black Phosphorus
• First-principles Phonon Calculations with Phonopy and Phono3py
• Slow Electrons in Polar Crystals: Self-Energy, Mass, and Mobility
• Diamond anvil cell and high-pressure physical investigations
• Structural, electronic, mechanical, and thermodynamic properties of Cu–Ti intermetallic compounds: First-principles calculations
• The role of alloying carbon on thermodynamic properties of ZrN: A first principle study
• Symmetry-Adapted Physical and Vibrational Properties of Ferroelectric Perovskite Oxides: Application to PbZrxTi1-xO3
• Relativism versus statistics in the microscopic foundation of thermodynamics
• Structural, electronic and mechanical properties ofCrN: A first principles study
• Stochastic Peierls-Nabarro Model for Dislocations in High Entropy Alloys
• Phase Transition of Iron-based Single Crystals at Extreme Strain Rates under Dynamic Loadings
• Exactly solvable model of sliding in metallic glass
• Convergence of a force-based hybrid method for atomistic and continuum models in three dimension
• Martensitic Transformation Precursors: Phonon Theory and Critical Experiments
• Active diffusing crystals in a 2D non-equilibrium system
• Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Study
• Tunable Electronic Transport in Pd₃O₂Cl₂ Kagome Bilayers: Interplay of Stacking Configuration and Strain
• Many-Body Correlation Effects in Fröhlich Electron-Phonon Coupling
• Infrared and Raman Studies of Long-Wavelength Optical Phonons in Hexagonal MoS2
• Electronic and elastic properties of the new 7.5K superconductor Nb2InC from first principles
• Exploring vibronic dynamics near a sloped conical intersection with trapped Rydberg ions
• In search of the electron-phonon contribution to total energy
• Refining Machine Learning Potentials through Thermodynamic Theory of Phase Transitions
• Anharmonic interaction as random field for thermal transport in FPU-β lattice
• Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions
• Electric Polarization from Nonpolar Phonons
• EPW-VASP interface for first-principles calculations of electron-phonon interactions
• Nonreciprocal Acoustic and Optical Phonon Dispersion Mediated by Berry Curvature in Chiral Weyl Semimetals
• Reststrahlen band and optical bandgaps in semiconducting CrN films
• Emergent elastic waves in skyrmion crystals with finite frequencies at long wavelength limit
• Non-perturbative Breakdown of Bloch's Theorem and Hermitian Skin Effects
• Ordered Phases of Diblock Copolymer Micelles in Selective Solvent
• Multiple Spawning with Optimal Basis Set Expansion
• Strain-Tunable Opto-electronics in PdS₂ Monolayer: the Role of Band Nesting and Carrier-Phonon Scattering
• Elastic and Strain--Tunable Electronic and Optical Properties of La2AlGaO6 Hybrid Perovskite: A First-Principles Study
• Hexagonal BeX (X: S, Te) monolayer as potential electrode material for alkali metal-ion batteries: A DFT perspective
• Phonon-based partition of (ZnSe-like) semiconductor mixed crystals on approach to their pressure-induced structural transition
• Some theoretical aspects of melting
• Where to Find ICEC? - Screening 2442 Systems for Interparticle Coulombic Electron Capture
• Granular and Nano-Elasticity
• Quantum Dynamics from Classical Trajectories
• Electrodynamics of nearly ferroelectric superconductors
• Single-Layer Di-titanium oxide Ti2O MOene: Multifunctional Promises for Electride, Anode Materials, and Superconductor
• Quasiharmonic lattice-dynamics and molecular-dynamics calculations for the Lennard-Jones solids
• Lattice-Dynamics Approach to the Theory of Elastic Dielectrics with Polarization Gradient
• Anankeon theory and viscosity of liquids: a toy model
• Electronic non-adiabatic states
• Crystal potentials under invariant periodic boundary conditions at\n infinity
• Thermoelectric transport and the role of different scattering processes in the half-Heusler NbFeSb
• Towards an effective potential for the monomer, dimer, hexamer, solid, and liquid forms of hydrogen fluoride
• First-Principles Investigation of the Physical and Thermoelectric Properties of Chalcogenide Compounds for Waste-Heat Recovery
• Long-lived electronic coherences in molecular wave packets probed with pulse-shape spectroscopy
• Finite temperature magnetic interactions from first principles
• Elastic properties of colloidal solids with disorder
• Pressure fluctuations in isotropic solids and fluids
• An atomistic/continuum coupling method using enriched bases
• Orbital-Engineered Spin Asymmetry and Multifunctionality in Eu-Activated CaAlSiN₃: A First-Principles Roadmap to Optical-Thermoelectric Fusion
• Pressure dependence of structural, elastic, electronic, thermodynamic, and optical properties of van der Waals-type NaSn2P2 pnictide superconductor: insights from DFT study
• Computing finite--temperature elastic constants with noise cancellation
• Conservative yet constitutively odd elasticity in prestressed metamaterials
• Beyond Hexagonal Boron Nitride: First-Principles Study of Pentaoctite-BN and Pop-BN Monolayers
• Theory of phonon-magnon hybridization and angular momentum in CrI₃ and CrBr₃
• Introduction to High-Resolution Inelastic X-Ray Scattering
• Phonons in nontransition metals
• OPTICAL STUDY OF THE CHARACTERISTICS OF SHOCK-COMPRESSED CONDENSED DIELECTRICS
• Ghost Force Influence of a Quasicontinuum Method in Two Dimension
• On the effect of ghost force in the quasicontinuum method: dynamic problems in one dimension
• Theory of the colossal Van-der-Waals binding in soft and hard condensed matter
• Jamming at zero temperature and zero applied stress: The epitome of disorder
• Spin relaxation of hot electrons in the Gamma-valley of zinc-blende semiconductors
• Exponential convergence of the local diabatic representation for nonadiabatic models
• Internal Stresses as Origin of the Anomalous Low-Temperature Specific Heat in Glasses
• A Priori Analysis of a Higher Order Nonlinear Elasticity Model for an Atomistic Chain with Periodic Boundary Condition
• Topological quantum correction to an atomic ideal gas law as a dark energy effect
• The mass and spin of the mesons, baryons and leptons
• A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations
• Temperature dependent phonon renormalization in metallic nanotubes
• Electronic-nuclear entanglement in Born-Oppenheimer wave functions and beyond
• Electric-field induced half-metallicity in a two-dimensional ferromagnetic Janus VSSe bilayer
• The total energy approach for calculating the specific heat of liquids and glasses
• Bulk modulus and equation of state
• Lattice vibrations in high-pressure phases of LiYF4
• An ab initio molecular dynamics exploration of associates in Ba-Bi liquid with strong ordering trends
• Dirichlet eta and beta functions at negative integer arguments: Exact results from anti-limits
• Stability of a force-based hybrid method with planar sharp interface
• Ab-initio heat transport in defect-laden quasi-1D systems from a symmetry-adapted perspective
• Interpolation of Microscale Stress and Strain Fields Based on Mechanical Models
• β-Irida-Graphene: A New 2D Carbon Allotrope for Sodium-Ion Battery Anodes
• Ab initio study of the elastic and electronic properties of tetragonal Th2NiC2
• First-principles phonon physics using the Pheasy code
• Quasi-Spin Ising Model and Monte Carlo Simulation of Ferroelastic Phase Transition: 3D Diffuse Scattering and Displacement Short-Range Ordering in Pre-Martensitic State
• Theoretical investigation of novel electronic, optical, mechanical and thermal properties of metallic hydrogen at 495 GPa
• A study on the quasiconinuum approximations of a one-dimensional fracture model
• Non-local elasticity theory as a continuous limit of 3D networks of pointwise interacting masses
• Elastic constants and supersolidity in solid hcp 4He
• Semiclassical analysis of quantum dynamics
• Realistic model for radiation-matter interaction
• Ti based half Heusler compounds: A new on the screen with robustic thermoelectric performance
• State Variables and Constraints in Thermodynamics of Solids and Their Implications
• Elucidating the impact of point defects on the structural, electronic, and mechanical behaviour of chromium nitride
• What are we talking about when we discuss the Born-Oppenheimer approximation?
• The plasma-solid transition:some implications in astrophysics
• Quantum Matter-Photonics Framework: Analyses of Chemical Conversion Processes
• Polarons in two-dimensional polar materials: All-coupling variational theory
• Dispersion of incoherent spectral features in systems with strong electron-phonon coupling
• Reversibility and hysteresis of the sharp yielding transition of a colloidal glass under oscillatory shear
• Long wavelength properties of electron-TO-phonon interactions in polar crystals
• A Practical Guide for Diagnosing Imaginary Phonon Modes in Metal--Organic Frameworks: The Case of MOF-5
• Cauchy problem for the localized wave propagation in continuous model of the one-dimensional diatomic crystal
• Data-driven high-throughput search for the accelerated discovery of rare-earth-free permanent magnets
• Anharmonic phonons via quantum thermal bath simulations
• Understanding paramagnetic spin correlations in the spin-liquid pyrochloreTb2Ti2O7
• Application of vibration-transit theory to distinct dynamic response for a monatomic liquid
• A solvable microscopic model for the propagation of light in a dielectric medium
• The Phase-Space Way To Electronic Structure Theory and Subsequently Chemical Dynamics
• Recovering Exact Vibrational Energies Within a Phase Space Electronic Structure Framework
• Ultralong Lifetime Plasmons on Picosecond Time Scale Enabled by Hybrid Plasmon-Phonon Polaritons
• Raman Scattering Due to Disorder-Induced Polaritons
• Realistic interatomic potential for MD simulations
• Theory of infrared magneto-optical effects from chiral phonons in solids
• A non-singular theory of dislocations in anisotropic crystals
• A thermodynamically consistent approach to describe the effect of thermal vacancy on abnormal thermodynamic behaviors of pure metals: application to body centered cubic W
• An analysis of emma's characters in the novel of the pye man viewed from psychoanalysis theory of freud
• Effect of strain and oxygen vacancies on the structure of 180^o ferroelectric domain walls in PbTiO₃
• Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants
• A New Laser Cooling Concept for Molecular Translational Motion
• Towards the microscopic foundation of the zeroth law of thermodynamics
• Magic of nonlocal geometric force: lighting up optical transition and transporting angular momentum by chiral phonons
• Dynamical Matrices and Interatomic-Force Constants from Wave-Commensurate Supercells
• Structural and mechanical properties of nitrogen-deficient cubic Cr-Mo-N and Cr-W-N systems
• Microscopic theory of phonon polaritons and long wavelength dielectric response
• Structural, Elastic, Electronic and Magnetic Properties of MnNbZ (Z=As, Sb) and FeNbZ (Z=Sn, Pb) Semi-Heusler Alloys
• Mechanical properties of lateral transition metal dichalcogenide heterostructures
• ElasTool: An automated toolkit for elastic constants calculation
• Lattice equations and dielectric function for optical lattice vibrations in monolayer transition metal dichalcogenides
• Theoretical Study of Elastic Far-Field Decay from Dislocations in Multilattices
• Theory of Rabi interaction between an infrared-active phonon and cavity-resonant modes
• On the microscopic foundations of elasticity
• Critical Integrated Raman Scattering Intensity near the cubic-tetragonal phase transition in Strontium Titanate
• On the time-dependent Born-Oppenheimer Approximation
• Theory of transformation for the diagonalization of quadratic Hamiltonians
• Quantum-mechanical theory of stress and force
• The plasma-solid transition
• Intrinsic stacking faults in body-centred cubic crystals
• Ab Initio Study of the Electronic Structure, Elastic Properties, Magnetic Feature and Thermodynamic Properties of the Ba2NiMoO6 Material
• A study of the mechanical and structural properties of polonium
• Phonon modes at finite temperature in graphene and single-walled carbon nanotubes
• Introduction to Solid State Physics
• The effect of pore structure on the local and nanoscale mobility of anisole and guaiacol in commercial zeolite catalysts
• Incremental constitutive tensors and strain localization for prestressed elastic lattices: Part I -- quasi-static response
• Translational invariance of Coulomb series and symmetric potentials in crystals
• Ultrahigh Intrinsic Hole Mobilities in MN₂ (M= Mo and W) at Room Temperature
• The Migdal effect in solid crystals and the role of non-adiabaticity
• Non-adiabatic molecular Hamiltonian: Canonical transformation coupling electronic and vibrational motions
• Chiral symmetry analysis and rigid rotational invariance for the lattice dynamics of single-wall carbon nanotubes
• The properties of iron under core conditions from first principles calculations
• Elasticity of Gaussian and nearly Gaussian phantom networks
• Multireference Approaches for Excited States of Molecules
• Vibrational and thermodynamic properties of high-pressure phases in LiYF₄
• Lattice Green function for extended defect calculations: Computation and error estimation with long-range forces
• Geophysics of Chemical Heterogeneity in the Mantle
• Ab initioquasiharmonic equations of state for dynamically stabilized soft-mode materials
• Two-phonon contributions to the inelastic x-ray scattering spectra ofMgB2
• Polaron action for multimode dispersive phonon systems
• Coulomb drag between a metal and a Wigner crystal
• Fast and slow thermal processes in harmonic scalar lattices
• Intrinsic vulnerabilities to mechanical failure in nanoscale films
• Low-temperature thermodynamics in the context of dissipative diamagnetism
• Intrinsic Chern Half-Metal with High Anomalous Hall Conductivity in 2D BaNiCl₃
• A mesoscopic model of a two-dimensional solid state structural transformation: statics and dynamics
• Chemical bonding, elasticity, and valence force field models: A case study forα−Pt2Siand PtSi
• Lattice dynamics and correlated atomic motion from the atomic pair distribution function
• Pressure-induced amorphization, crystal-crystal transformations, and the memory glass effect in interacting particles in two dimensions
• Phonons and specific heat of linear dense phases of atoms physisorbed in the grooves of carbon nanotube bundles
• Ab initiostudies of solid bromine under high pressure
• Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory
• Carbon-doped K4 nitrogen: A novel high energy density material
• Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of theTb2Ti2O7pyrochlore antiferromagnet
• Elastic fluctuations as observed in a confocal slice
• A reactive force field for lithium–aluminum silicates with applications to eucryptite phases
• Multiphonon Raman scattering in semiconductor nanocrystals: Importance of nonadiabatic transitions
• Structural, elastic, thermal, and electronic responses of small-molecule-loaded metal–organic framework materials
• On a nearly proton-ordered structure for ice IX
• Dynamical stability of iron under high-temperature and high-pressure conditions
• Scattering of Holes by Phonons in Germanium
• Monolayer C₆₀ networks: A first-principles perspective
• Kinetic Isotope Effects for the Reactions of Muonic Helium and Muonium with H 2
• Cheon’s anholonomies in Floquet operators
• A DFT study on 18-crown-6-like-N₈ structure as a material for metal-ions storage: stability and performance
• Orientational ordering of local shear stresses in liquids: A phase transition?
• Spin transport theory in ferromagnet/semiconductor systems with noncollinear magnetization configurations
• The Soul of Waves: Physical Interpretation of Dispersion Relations
• On the two-dimensional hydrogen atom in a circular box in the presence of an electric field
• Concept of local polaritons and optical properties of mixed polar crystals
• Tunable topological phase in 2D ScV₆Sn₆ kagome material
• A Molecular Dynamics Study of the Thermodynamic Properties of Calcium Apatites. 1. Hexagonal Phases
• Molecular Dynamics Study of the Thermodynamic Properties of Calcium Apatites. 2. Monoclinic Phases
• Testing the Newton second law in the regime of small accelerations
• Elastic, Quasielastic, and Superelastic Electron Scattering from Thermal Lattice Distortions in Perfect Crystals
• Small and large scale granular statics
• Tangential-force model for interactions between bonded colloidal particles
• Shear-strain and shear-stress fluctuations in generalized Gaussian ensemble simulations of isotropic elastic networks
• Interatomic repulsion softness directly controls the fragility of supercooled metallic melts
• Physics-Informed Machine Learning for Refractory Alloy Design
• Adiabatic electronic flux density: A Born-Oppenheimer broken-symmetry ansatz
• Nonlocal effects on the resonant dielectric surface observed by near-field optical probing in mid-infrared range
• K-dependent exchange interaction of the1Sorthoexciton inCu2O
• Lattice-switch Monte Carlo method
• Elastic moduli and vibrational modes in jammed particulate packings
• Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation
• Mechanism of electromagnetic emission in plastically deformed ionic crystals
• Consistency between the Green-Kubo formula and Lorentz model for predicting the infrared dielectric function of polar materials
• Perturbative quantum Monte Carlo study ofLiHoF4in a transverse magnetic field
• Explaining the specific heat of liquids based on instantaneous normal modes
• Linear and nonlinear optics of surface-plasmon whispering-gallery modes
• Degenerate ground state in the classical pyrochlore antiferromagnetNa3Mn(CO3)2Cl
• Pre-Born–Oppenheimer molecular structure theory
• On the critical nature of plastic flow: One and two dimensional models
• Effects of shear flow on phase nucleation and crystallization
• Theoretical investigation of magnetoelectric behavior inBiFeO3
• Characterization of zero-point vibration in one-component crystals
• Electronic structures and mechanical properties of boron and boron-rich crystals (Part 2)
• Anisotropy and phonon modes from analysis of the dielectric function tensor and the inverse dielectric function tensor of monoclinic yttrium orthosilicate
• Phonons and related crystal properties from density-functional perturbation theory
• Modeling of Phase Separation in Alloys with Coherent Elastic Misfit
• Exploring the Many-Body Dynamics Near a Conical Intersection with Trapped Rydberg Ions
• First‐principles prediction of mechanical and bonding characteristics of new T2 superconductor Ta5GeB2
• High-Performance Thermoelectric Oxides Based on Spinel Structure
• Lifetimes of confined optical phonons and the shape of a Raman peak in disordered nanoparticles. I. Analytical treatment
• A review on the flexural mode of graphene: lattice dynamics, thermal conduction, thermal expansion, elasticity and nanomechanical resonance
• Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean-free paths
• Symmetries and Dualities in the Theory of Elasticity
• Vibrational Contribution to Density and Current Autocorrelations in a Monatomic Liquid
• Conditions for the existence of phonon localized edge-modes
• Relaxation times and ergodic properties in a realistic ionic-crystal model, and the modern form of the FPU problem
• Strongly Enhanced Raman Optical Activity in Molecules by Magnetic Response of Nanoparticles
• Prawo łaski Prezydenta RP
• Ab initioinvestigation of the elasticity and stability of aluminium
• Structural transition of a Wigner crystal on a liquid substrate
• Temperature-dependent effective third-order interatomic force constants from first principles
• Machine learning on neutron and x-ray scattering and spectroscopies
• Superconductivity in SrTiO3: Dielectric Function Method for Non-Parabolic Bands
• Heat capacity and thermal expansion of metal crystalline materials based on dynamic thermal vibration
• The β-decay spectrum of Tritiated graphene: combining nuclear quantum mechanics with Density Functional Theory
• Construction and application of multi-element EAM potential (Ni–Al–Re) inγ/γ′ Ni-based single crystal superalloys
• Elasticity of bidisperse attractive particle systems
• Polarizing Oxygen Vacancies in Insulating Metal Oxides under a High Electric Field
• Elastic anisotropy and Surface Acoustic Wave propagation in CoFeB/Au multilayers: influence of thickness and light penetration depth
• Towards a predictive first-principles description of solid molecular hydrogen with density functional theory
• Exploring Multifunctional Applications of Hexagonal Boron Arsenide Sheet: A DFT Study. [europepmc]
• Inspecting the electronic structure and thermoelectric power factor of novel p-type half-Heuslers. [europepmc]
• Structural evolution and phase transition mechanism of [Formula: see text] under high pressure. [europepmc]
• Status and Challenges in Homogenization Methods for Lattice Materials. [europepmc]
• Lattice Dynamics, Mechanical Properties, Electronic Structure and Magnetic Properties of Equiatomic Quaternary Heusler Alloys CrTiCoZ (Z = Al, Si) Using First Principles Calculations. [europepmc]
• Coherent interfaces govern direct transformation from graphite to diamond. [europepmc]
• Structural, Electronic, Mechanical, and Thermodynamic Properties of Na Deintercalation from Olivine NaMnPO 4 : First-Principles Study. [europepmc]
• Phonon transport in Janus monolayer siblings: a comparison of 1T and 2H-ISbTe. [europepmc]
• Single Crystals of EuScCuSe 3 : Synthesis, Experimental and DFT Investigations. [europepmc]
• Ferro-piezoelectricity in emerging Janus monolayer BMX 2 (M = Ga, In and X = S, Se): ab initio investigations. [europepmc]
• Doping Engineering for Optimizing Piezoelectric and Elastic Performance of AlN. [europepmc]
• Exploring structural, mechanical, and thermoelectric properties of half-Heusler compounds RhBiX (X = Ti, Zr, Hf): A first-principles investigation. [europepmc]
• Robust Inversion of Time-Resolved Data via Forward-Optimization in a Trajectory Basis. [europepmc]
• First-principles examination of two-dimensional Janus quintuple-layer atomic structures XCrSiN 2 (X = S, Se, and Te). [europepmc]
• Investigation of the Influence of Pressure on the Physical Properties and Superconducting Transition Temperature of Chiral Noncentrosymmetric TaRh 2 B 2 and NbRh 2 B 2 . [europepmc]
• Tunable Contact Types and Interfacial Electronic Properties in TaS 2 /MoS 2 and TaS 2 /WSe 2 Heterostructures. [europepmc]
• Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics. [europepmc]
• Single-Layer GaInSe 3 : Promising Water-Splitting Photocatalyst with Solar Conversion Efficiency over 30% from Theoretical Calculations. [europepmc]
• Influence of Mg Doping on the Structure and Mechanical Properties of Al 2 Cu Precipitated Phase by First-Principles Calculations. [europepmc]
• Coupled Electron-Nuclear Dynamics Induced and Monitored with Femtosecond Soft X-ray Pulses in the Amino Acid Glycine. [europepmc]
• Combined First-Principles and Experimental Investigation into the Reactivity of Codeposited Chromium-Carbon under Pressure. [europepmc]
• Large piezoelectric responses and ultra-high carrier mobility in Janus HfGeZ 3 H (Z = N, P, As) monolayers: a first-principles study. [europepmc]
• Janus MoSH/WSi 2 N 4 van der Waals Heterostructure: Two-Dimensional Metal/Semiconductor Contact. [europepmc]
• Structural and electronic features enabling delocalized charge-carriers in CuSbSe 2 . [europepmc]
• Novel auxetic semiconductors with high carrier mobility: first principles prediction of Janus Ge 2 XY (X/Y = S, Se, Te) monolayers. [europepmc]

Related

• Nonlinear Waves in Lattices: Past, Present, Future
• Wave theory of lattice dynamics
• Dynamical Matrices and Interatomic-Force Constants from Wave-Commensurate Supercells
• Classical microscopic theory of dispersion, emission and absorption of light in dielectrics
• Lattice Gauge Theories