000			03609nam a22005055i 4500
001			978-3-319-29977-8
003			DE-He213
005			20190213151533.0
007			cr nn 008mamaa
008			160628s2016 gw | s |||| 0|eng d
020			_a9783319299778 _9978-3-319-29977-8
024	7		_a10.1007/978-3-319-29977-8 _2doi
050		4	_aQA370-380
072		7	_aPBKJ _2bicssc
072		7	_aMAT007000 _2bisacsh
072		7	_aPBKJ _2thema
082	0	4	_a515.353 _223
100	1		_aGesztesy, Fritz. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	4	_aThe Callias Index Formula Revisited _h[electronic resource] / _cby Fritz Gesztesy, Marcus Waurick.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2016.
300			_aIX, 192 p. 1 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes in Mathematics, _x0075-8434 ; _v2157
505	0		_aIntroduction.-Notational Conventions -- Functional Analytic -- On Schatten–von Neumann Classes and Trace Class -- Pointwise Estimates for Integral Kernels -- Dirac-Type -- Derivation of the Trace Formula – The Trace Class Result -- Derivation of the Trace Formula – Diagonal Estimates -- The Case n = 3 -- The Index Theorem and Some Consequences -- Perturbation Theory for the Helmholtz Equation -- The Proof of Theorem 10.2: The Smooth Case -- The Proof of Theorem 10.2: The General Case -- A Particular Class of Non-Fredholm Operators L and Their Generalized Witten Index -- A: Construction of the Euclidean Dirac Algebra -- B: A Counterexample to [22, Lemma 5] -- References -- Index.
520			_aThese lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970’s, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.
650		0	_aDifferential equations, partial.
650		0	_aOperator theory.
650		0	_aFunctional analysis.
650	1	4	_aPartial Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12155
650	2	4	_aOperator Theory. _0http://scigraph.springernature.com/things/product-market-codes/M12139
650	2	4	_aFunctional Analysis. _0http://scigraph.springernature.com/things/product-market-codes/M12066
700	1		_aWaurick, Marcus. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319299761
776	0	8	_iPrinted edition: _z9783319299785
830		0	_aLecture Notes in Mathematics, _x0075-8434 ; _v2157
856	4	0	_uhttps://doi.org/10.1007/978-3-319-29977-8
912			_aZDB-2-SMA
912			_aZDB-2-LNM
999			_c11014 _d11014