This chapter discusses two major developments that have taken place over the past decade. First is the enormous wealth of energy band calculations that have had tremendous success in explaining the properties of specific solids, but in which the connection with first principles is not always apparent. Second is the spectacular progress of many-body theory applied to the solid state that has given a number of new results, although often of a rather general and formal nature, such as to provide the justification and a formal basis for a one-electron theory. The electron gas problem is treated in some detail here. The problem of the crystal potential is given due attention. It discusses the potential from the ion cores as well as from the valence electrons, and suggests schemes that incorporate essential exchange and correlation effects for the valence electrons. An energy band calculation that properly includes the effects of exchange and correlation describes the elementary excitations called quasi particles. Quasi-particle properties are usually discussed using the remarkable Landau theory of the Fermi liquid. This chapter gives a brief presentation of the theory and reviews the present status of calculations of the Fermi liquid parameters and how they are determined from experiments.}, author = {Hedin, Lars and Lundqvist, Stig O.}, editor = {Seitz, Frederick and Turnbull, David and Ehrenreich, Henry}, isbn = {978-0-12-607723-0}, language = {eng}, pages = {1--181}, publisher = {Academic Press}, series = {Solid State Physics}, title = {Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids}, uurl = {http://dx.doi.org/10.1016/S0081-1947(08)60615-3}, volume = 23, year = 1969, } @book{hehl80b, AUTHOR = "F.W.~Hehl", TITLE = "Four lectures on the Poincar\'e gauge field theory", BOOKTITLE = "Cosmology and Gravitation", EDITOR = "P.G.~Bergmann and V.~De Sabbata", YEAR = 1980 } @article{heis36-98-714, author = {W. Heisenberg and H. Euler}, title = {Consequences of {D}irac's theory of positrons}, journal = {Z. Phys.}, year = 1936, volume = 98, pages = {714-732}, slaccitation = {%%CITATION = ZEPYA,98,714;%%} } @book{hejh76b, AUTHOR = "D.A.~Hejhal", TITLE = "The Selberg Trace Formula for PSL(2,R)", PUBLISHER = "Springer-Verlag, Berlin", YEAR = 1976 } @book{helg84b, AUTHOR = "S. Helgason", TITLE = "Group and Geometric Analysis", PUBLISHER = "Academic Press Inc.", YEAR = 1984 } @article{hell86-34-1918, author = {Helliwell, TM and Konkowski, DA}, file = {:D$\backslash$:/User/Bordag/WORK/Literatur/Papers\_pdf\_files/p1918\_1.pdf:pdf}, journal = prd, number = 6, pages = {1918--1920}, title = {{Vacuum fluctuations outside cosmic strings}}, uuurll = {http://prd.aps.org/abstract/PRD/v34/i6/p1918\_1}, volume = 34, year = 1986 } @book{hemp76b, AUTHOR = "J.~Hempel", TITLE = "3-Manifolds", BOOKTITLE = "Ann.~of Math.~Studies", PUBLISHER = "Princeton Univ.~Press", VOLUME = 86, YEAR = 1976 } @article{heng05-15-026105, author = {Hänggi,Peter and Ingold,Gert-Ludwig }, title = {Fundamental aspects of quantum Brownian motion}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = 15, number = 2, pages = 026105, year = 2005, doi = {10.1063/1.1853631}, URL = { https://doi.org/10.1063/1.1853631 }, eprint = { https://doi.org/10.1063/1.1853631 } } @article{henk00-186-57, title = "Spatial coherence of thermal near fields", journal = "Optics Communications", volume = 186, number = 1, pages = "57 - 67", year = 2000, issn = "0030-4018", doi = "https://doi.org/10.1016/S0030-4018(00)01048-8", uurl = "http://www.sciencedirect.com/science/article/pii/S0030401800010488", author = "C. Henkel and K. Joulain and R. Carminati and J.-J. Greffet", keywords = "Black body radiation", keywords = "Polaritons", keywords = "Surface plasmons", keywords = "Coherence in wave optics", keywords = "Scanning near-field optical microscopy" } @article{henk08-78, author = {Carsten Henkel and Baruch Horovitz}, title = {Noise from metallic surfaces: Effects of charge diffusion}, journal = {Phys. Rev. A}, year = 2008, volume = 78, pages = 042902, abstract = {We study electromagnetic response functions for metallic surfaces with diffusive carrier transport. The electric field noise at a distance