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| 001 | 0093767144▲ | ||
| 005 | 20180519023119▲ | ||
| 008 | 160118s2016 sz b 001 0 eng c▲ | ||
| 010 | ▼a2016942549▲ | ||
| 020 | ▼a9783319299761 (paperback)▲ | ||
| 020 | ▼a331929976X (paperback)▲ | ||
| 020 | ▼z9783319299778 (eBook)▲ | ||
| 040 | ▼aYDXCP▼beng▼cYDXCP▼dBTCTA▼dOCLCQ▼dOCLCO▼dORE▼dOHX▼dOCLCF▼dUMS▼dPAU▼dTJC▼dEQO▼dMYG▼d221016▲ | ||
| 050 | 4 | ▼aQA3▼b.L37 no.2157▲ | |
| 072 | 7 | ▼aQC▼2lcco▲ | |
| 072 | 7 | ▼aQA▼2lcco▲ | |
| 082 | 0 | 4 | ▼a514.74▼223▲ |
| 090 | ▼a514.74▼bG393c▲ | ||
| 100 | 1 | ▼aGesztesy, Fritz,▼d1953-▲ | |
| 245 | 1 | 4 | ▼aThe Callias index formula revisited /▼cFritz Gesztesy, Marcus Waurick.▲ |
| 260 | ▼a[Cham] Switzerland :▼bSpringer,▼c[2016]▲ | ||
| 300 | ▼aix, 192 p. ;▼c24 cm.▲ | ||
| 490 | 1 | ▼aLecture notes in mathematics,▼x0075-8434 ;▼v2157▲ | |
| 504 | ▼aIncludes bibliographical references (p. 185-189) and index.▲ | ||
| 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].▲ | |
| 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 | ▼aIndex theorems.▲ | |
| 650 | 0 | ▼aDifferential equations, Partial.▲ | |
| 700 | 1 | ▼aWaurick, Marcus.▲ | |
| 830 | 0 | ▼aLecture notes in mathematics (Springer-Verlag) ;▼v2157.▲ | |
| 999 | ▼a김진영▼c김정이▲ |
The Callias index formula revisited
자료유형
국외단행본
서명/책임사항
The Callias index formula revisited / Fritz Gesztesy, Marcus Waurick.
발행사항
[Cham] Switzerland : Springer , [2016]
형태사항
ix, 192 p. ; 24 cm.
총서사항
Lecture notes in mathematics , 0075-8434 ; 2157
Lecture notes in mathematics (Springer-Verlag) ; 2157.
Lecture notes in mathematics (Springer-Verlag) ; 2157.
서지주기
Includes bibliographical references (p. 185-189) and index.
내용주기
Introduction -- 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].
요약주기
These 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.
ISBN
9783319299761 (paperback) 331929976X (paperback)
청구기호
514.74 G393c
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