À propos de mathématiques
A propos d’anomalies en mathématique et en physique
Femmes & math, Tome 7 (2004), pp. 51-66.

Nous montrons comment des anomalies « traciales » du côté des mathématiques peuvent se manifester en théorie des champs. Cette présentation est basée sur un article en collaboration avec A. Cardona et C. Ducourtioux [4].

Publié le :
Paycha, Sylvie 1

1 Département de Mathématiques Appliquées Complexe universitaire des Cézeaux Université Blaise Pascal 63177 Aubière cedex France
@article{RFM_2004__7__51_0,
     author = {Paycha, Sylvie},
     title = {A propos d{\textquoteright}anomalies en math\'ematique et en physique},
     journal = {Femmes & math},
     pages = {51--66},
     publisher = {Association femmes et math\'ematiques},
     volume = {7},
     year = {2004},
     language = {fr},
     url = {http://www.numdam.org/item/RFM_2004__7__51_0/}
}
TY  - JOUR
AU  - Paycha, Sylvie
TI  - A propos d’anomalies en mathématique et en physique
JO  - Femmes & math
PY  - 2004
SP  - 51
EP  - 66
VL  - 7
PB  - Association femmes et mathématiques
UR  - http://www.numdam.org/item/RFM_2004__7__51_0/
LA  - fr
ID  - RFM_2004__7__51_0
ER  - 
%0 Journal Article
%A Paycha, Sylvie
%T A propos d’anomalies en mathématique et en physique
%J Femmes & math
%D 2004
%P 51-66
%V 7
%I Association femmes et mathématiques
%U http://www.numdam.org/item/RFM_2004__7__51_0/
%G fr
%F RFM_2004__7__51_0
Paycha, Sylvie. A propos d’anomalies en mathématique et en physique. Femmes & math, Tome 7 (2004), pp. 51-66. http://www.numdam.org/item/RFM_2004__7__51_0/

[1] R. Baadhio, Quantum Topology and Global Anomalies, Adv. Ser. in Math. Phys. 23, World Scientific, 1996. | MR | Zbl

[2] R. Bertlmann, Anomalies in Quantum Field Theory, Oxford University Press, 1996. | MR | Zbl

[3] J.M. Bismut, D. Freed, The analysis of elliptic families I and II, Comm. Math. Phys. 106, 159-176, et Comm. Math. Phys. 107, 103-163 (1986). | MR | Zbl

[4] A. Cardona, C. Ducourtioux, S. Paycha, From tracial anomalies to anomalies in quantum field theory, Comm. Math. Phys. 242, 31-65 (2003). | MR | Zbl

[5] A. Cardona, C. Ducourtioux, J. P. Magnot, S. Paycha, Weighted traces on algebras of pseudodifferential operators and geometry of loop groups, Infin. Dimens. Anal. Quantum Probab. and Relat. Top. 5, 503-540 (2002). | MR | Zbl

[6] C. Ducourtioux, Weighted traces on pseudo-differential operators and associated determinants, Thèse de Doctorat de l’Université Blaise Pascal, 2001.

[7] P. Deligne, P. Etinghof, D. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D. Morrison, E. Witten, Quantum Fields and Strings : A Course for Mathematicians, American Mathematical Society, 1999. | MR | Zbl

[8] D. Freed, Determinants, torsion, and strings, Comm. Math. Phys. 107, 487-525 (1987). | MR | Zbl

[9] M. Kontsevich, S. Vishik, Geometry of determinants of elliptic operators, Func. Anal. on the Eve of the XXI Century, Vol. I, Progress in Mathematics 131, 173-197 (1994). | MR | Zbl

[10] J. Mickelsson, Wodzicki residue and anomalies on current algebras in Integrable Models and Strings, A. Alekseer ed., Lecture Notes in Physics 436, Springer, 1994. | MR | Zbl

[11] R. Melrose and V. Nistor, Homology of pseudo-differential operators I. Manifolds with boundary, Preprint funct.an 96 06 005, juin 99.

[12] M. Nakahara, Geometry, Topology and Physics, Graduate Student Series in Physics, 1990. | MR | Zbl

[13] K. Okikiolu, The multiplicative anomaly for determinants of elliptic operators, Duke Math. Journ. 79, 723-750 (1995) ; K. Okikiolu, The Campbell-Hausdorff theorem for elliptic operators and a related trace formula, Duke Math. Journ. 79, 687-722 (1995). | MR | Zbl

[14] S. Paycha, Renormalized traces as a looking glass into infinite dimensional geometry, Infin. Dimens. Anal. Quantum Probab. and Relat. Top. 4, 221-266 (2001). | MR | Zbl

[15] S. Paycha, S. Rosenberg, Curvature on determinant bundles and first Chern forms, Journ. Geom. Phys. 45, 393-429 (2003). | MR | Zbl

[16] D. Quillen, Determinants of Cauchy-Riemann operators over a Riemann surface, Funktsional Anal. i Prilozhen. 19, 37-41 (1985). | MR | Zbl

[17] D. Quillen, Superconnections and the Chern character, Topology 24, 89-95 (1985). | MR | Zbl

[18] A.O. Radul, Lie algebras of differential operators, their central extensions and W-algebras, Funct. Anal. Appl. 25, 25-39 (1992). | MR | Zbl

[19] E. Witten, Global gravitational anomalies, Comm. Math. Phys. 100, 197-229 (1985). | MR | Zbl

[20] M. Wodzicki, Non commutative residue, in K-theory, Arithmetic and Geometry, Moscow University, 1984-1986, Yu.I.Manin ed., Lecture Notes in Math. 1283, Springer Verlag, 1987. | MR | Zbl