02569nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100003300213245010700246260008200353300003400435336002600469337002600495338003600521347002400557490005000581506006600631520125200697650004801949650002401997650004002021650004802061856003202109856006602141245-191015CH-001817-320191015233004.0a fot ||| 0|cr nn mmmmamaa191015e20191115sz fot ||| 0|eng d a978303719594970a10.4171/0942doi ach0018173 7aPHT2bicssc a81-xxa35-xxa58-xx2msc1 aGérard, Christian,eauthor.10aMicrolocal Analysis of Quantum Fields on Curved Spacetimesh[electronic resource] /cChristian Gérard3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (228 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aWe focus on free fields and the corresponding quasi-free states and more precisely on Klein–Gordon fields and Dirac fields. The first chapters are devoted to preliminary material on CCR*-algebras, quasi-free states, wave equations on Lorentzian manifolds, microlocal analysis and to the important Hadamard condition, characterizing physically acceptable quantum states on curved spacetimes. In the later chapters more advanced tools of microlocal analysis, like the global pseudo-differential calculus on non-compact manifolds, are used to construct and study Hadamard states for Klein–Gordon fields by various methods, in particular by scattering theory and by Wick rotation arguments. In the last chapter the fermionic theory of free Dirac quantum fields on Lorentzian manifolds is described in some detail.
This monograph is addressed to both mathematicians and mathematical physicists. The first will be able to use it as a rigorous exposition of free quantum fields on curved spacetimes and as an introduction to some interesting and physically important problems arising in this domain. The second may find this text a useful introduction and motivation to the use of more advanced tools of microlocal analysis in this area of research.07aQuantum physics (quantum mechanics)2bicssc07aQuantum theory2msc07aPartial differential equations2msc07aGlobal analysis, analysis on manifolds2msc40uhttps://doi.org/10.4171/094423cover imageuhttps://www.ems-ph.org/img/books/gerard_mini.jpg