Families of Dirac operators with applications to physics

Singer, I. M.

Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984, Astérisque, no. S131 (1985), pp. 323-340

MR Zbl

@incollection{AST_1985__S131__323_0,
     author = {Singer, I. M.},
     title = {Families of {Dirac} operators with applications to physics},
     booktitle = {\'Elie Cartan et les math\'ematiques d'aujourd'hui - Lyon, 25-29 juin 1984},
     series = {Ast\'erisque},
     pages = {323--340},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {S131},
     year = {1985},
     mrnumber = {837207},
     zbl = {0603.58054},
     language = {en},
     url = {https://www.numdam.org/item/AST_1985__S131__323_0/}
}

TY  - CHAP
AU  - Singer, I. M.
TI  - Families of Dirac operators with applications to physics
BT  - Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984
AU  - Collectif
T3  - Astérisque
PY  - 1985
SP  - 323
EP  - 340
IS  - S131
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_1985__S131__323_0/
LA  - en
ID  - AST_1985__S131__323_0
ER  -

%0 Book Section
%A Singer, I. M.
%T Families of Dirac operators with applications to physics
%B Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984
%A Collectif
%S Astérisque
%D 1985
%P 323-340
%N S131
%I Société mathématique de France
%U https://www.numdam.org/item/AST_1985__S131__323_0/
%G en
%F AST_1985__S131__323_0

Singer, I. M. Families of Dirac operators with applications to physics, dans Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984, Astérisque, no. S131 (1985), pp. 323-340. https://www.numdam.org/item/AST_1985__S131__323_0/

Bibliographie
Cité par

[1] Alvarez (O.) and Singer (I. M.). - Still another view of chiral anomalies, in preparation.

[2] Alvarez (O.), Singer (I. M.) and Zumino (B.). - Gravitational Anomalies and the Family's Index Theorem, Comm. Math. Phys., t. 96, 1984, p. 409. | MR | Zbl | DOI

[3] Atiyah (M. F.), Patodi (V. K.) and Singer (I. M.). - Spectral asymmetry and Riemannian geometry II, Math. Proc. Camb. Phil. Soc., t. 78, 1975, p. 405. | MR | Zbl | DOI

[4] Atiyah (M. F.) and Singer (I. M.). - Dirac operators coupled to vector potentials, Proc. Nat. Acad. Sci. USA, t. 81, 1984, p. 2597. | MR | Zbl | DOI

[5] Atiyah (M. F.) and Singer (I. M.). - Index Theory for skew-adjoint Fredholm Operators, Pub. Math. IHES, t. 37, 1969, p. 305. | Zbl | MR | EuDML | Numdam

[6] Bonora (L.), Cotta-Ramusino (P.). - Some remarks on B.R.S. transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations, Comm. Math. Phys., t. 87, 1983, p. 589. | MR | Zbl | DOI

[7] Chern (S. S.). - Geometry of Characteristic Classes, Appendix, Complex Manifolds without Potential Theory. - Springer, N.Y. 1979. | MR

[8] Chern (S. S.) and Simons (J.). - Characteristic forms and geometric invariants, Ann. of Math., t. 99, 1974, p. 48. | MR | Zbl | DOI

[9] Connes (A.). - Cohomologue cyclique et foncteurs ${Ext}^{n}$ , C. R. Acad. Sci. Paris, t. 296, 1983, p. 953. | MR | Zbl

[10] Deser (S.), Jackiw (R.) and Templeton (S.). - Three Dimensional Massive Gauge Theories, Ann. Phys. (NY), t. 140, 1982, p. 372. | MR | DOI

[11] Fadeev (L.). - Operational Anomalies for the Gauss law, Phys. Lett., t. 14B, 1984, p. 81. | DOI

[12] Frenkel (I. B.) and Kac (V.). - Basic representations of affine Lie algebras and dual resonance models, Invent. Math., t. 62, 1980, p. 23. | MR | Zbl | EuDML | DOI

[13] Hawking (S. W.). - Zeta function regularization of path integrals in curved spacetime, Comm. Math. Phys., t. 55, 1977, p. 133. | MR | Zbl | DOI

[14] Jackiw (R.). - (a) Quantization of Physical Parameters, Comments Nuclear and Particle Physics, t. 13, 1984, p. 15

Jackiw (R.). - (b) Fractional Fermions, (Comments Nuclear and Particle Physics, t. 13, 1984, p. 141).

[15] Loday (J. L.) and Quillen (D.). - Cyclic homology and the Lie algebra homology of matrices, preprint. | MR | Zbl

[16] Lott (J.). - A proof of axial anomaly, Harvard preprint. | Zbl

[17] Quillen (D.). - Determinants of Cauchy-Riemann Operators on a Riemann surface, IHES preprint, July 1984. | MR | Zbl

[18] Ramadas (T. R.). - The Wess-Zumino term and fermionic solitons, Comm. Math. Phys., t. 93, 1984, p. 355. | MR | Zbl | DOI

[19] Ray (D.) and Singer (I. M.). - $R$ -torsion and the Laplacian on Riemannian Manifolds, Adv. in Math., t. 7, 1971, p. 145. | MR | Zbl | DOI

[20] Seeley (R. T.). - Complex powers of an elliptic operator, Amer. Math. Soc. Proc. Sym. Pure Math., t. 10, 1967, p. 288. | MR | Zbl | DOI

[21] Segal (G.). - Unitary representations of some infinite dimensional groups, Comm. Math. Phys., t. 80, 1981, p. 301. | MR | Zbl | DOI

[22] Singer (I. M.). - Some remarks on the Gribov ambiguity, Comm. Math. Phys., t. 60, 1978, p. 7. | MR | Zbl | DOI

[23] Vafa (C.) and Witten (E.). - Eigenvalue inequalities for fermions in gauge theories, preprint Joseph Henry Lab. Princeton Apr. 1984. | MR

[24] Wess (J.) and Zumino (B.). - Consequences of Anomalous Ward Identities, Phys. Lett., t. 37 B, 1971, p. 95. | MR | DOI

[25] Witten (E.). - Global aspects of current algebra, Nuc. Phys. B, t. 223, 1983, p. 422. | MR | DOI

[26] Witten (E.). - An $S U (2)$ anomaly, Phys. Lett., t. 117 B, 1982, p. 324. | MR | DOI