02601nmm a2200445 i 4500991003325579707536cr cn ---mpcbr170207s2014 sz | o j |||| 0|eng d9783319024417 (ebook)10.1007/978-3-319-02441-7doib14316250-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng516.3623AMS 53C55AMS 32G07AMS 32Q55AMS 32Q60AMS 53D18LC QA3.L28Angella, Daniele524797Cohomological Aspects in Complex Non-Kähler Geometry[e-book] /by Daniele AngellaCham :Springer Intern. Publ.,20141 online resourcetexttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture Notes in Mathematics,1617-9692 ;2095Preliminaries on (almost-) complex manifolds ; Cohomology of complex manifolds ; Cohomology of nilmanifolds ; Cohomology of almost-complex manifolds ; ReferencesIn these notes, we provide a summary of recentresults on the cohomological properties of compact complex manifolds not endowed with a Kähler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kähler structure. We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also consideredDifferential equations, partialGlobal differential geometrySpringer eBooksPrinted edition:9783319024400http://link.springer.com/book/10.1007/978-3-319-02441-7An electronic book accessible through the World Wide.b1431625003-03-2207-02-17991003325579707536Cohomological aspects in complex non-Kähler geometry820739UNISALENTOle01307-02-17m@ -engsz 0004042nam 22007095 450 991073946440332120230629193212.03-030-69105-510.1007/978-3-030-69105-9(CKB)4100000011949991(MiAaPQ)EBC6633367(Au-PeEL)EBL6633367(OCoLC)1253477471(DE-He213)978-3-030-69105-9(PPN)255883285(EXLCZ)99410000001194999120210529d2021 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe Development of the Action Principle A Didactic History from Euler-Lagrange to Schwinger /by Walter Dittrich1st ed. 2021.Cham :Springer International Publishing :Imprint: Springer,2021.1 online resource (141 pages)SpringerBriefs in Physics,2191-54313-030-69104-7 Short Historical Introduction -- Curva Elastica -- The Curva Elastica, a Curve of Least Energy -- From Euler to Lagrange -- Laplace and the Capillary - 1807 -- A Final Application in Elasticity with Jacobi Elliptic Functions -- Short List of Jacobi Elliptic Functions and Constants Used in Chapter 5 -- Variational Methods for Periodic Motions; Mathieu Functions -- Lagrangian for Isentropic Irrotational Flow -- Action Principle in Classical Electrodynamics -- The Two Giants in Gravity: Einstein and Hilbert -- The Quantum Action Principle -- The Action Principle in Quantum Field Theory -- Quantum Field Theory on Space-Like Hypersurfaces -- Lagrangian Formulation of Gauge Theories -- Effective Actions (Lagrangians) in Quantum Field Theory -- Modified Photon Propagation Function, Source Theory.This book describes the historical development of the principle of stationary action from the 17th to the 20th centuries. Reference is made to the most important contributors to this topic, in particular Bernoullis, Leibniz, Euler, Lagrange and Laplace. The leading theme is how the action principle is applied to problems in classical physics such as hydrodynamics, electrodynamics and gravity, extending also to the modern formulation of quantum mechanics and quantum field theory, especially quantum electrodynamics. A critical analysis of operator versus c-number field theory is given. The book contains many worked examples. In particular, the term "vacuum" is scrutinized. The book is aimed primarily at actively working researchers, graduate students and historians interested in the philosophical interpretation and evolution of physics; in particular, in understanding the action principle and its application to a wide range of natural phenomena.SpringerBriefs in Physics,2191-5431MechanicsPhysics—HistoryMathematical physicsParticles (Nuclear physics)Quantum field theoryPhysics—PhilosophyClassical MechanicsHistory of Physics and AstronomyMathematical PhysicsElementary Particles, Quantum Field TheoryPhilosophical Foundations of Physics and AstronomyMechanics.Physics—History.Mathematical physics.Particles (Nuclear physics)Quantum field theory.Physics—Philosophy.Classical Mechanics.History of Physics and Astronomy.Mathematical Physics.Elementary Particles, Quantum Field Theory.Philosophical Foundations of Physics and Astronomy.530.1209Dittrich Walter46017MiAaPQMiAaPQMiAaPQBOOK9910739464403321The Development of the Action Principle2005655UNINA