Michael Müger

Some recent presentations

- LMS Meeting and Workshop on Operator Algebras and Physics, Cardiff 21.-25.6.2010: Superselection theory in low dimensions, modular invariants and categorical ramifications
(This is an extended version of my talk at the ICMP Prague, 2009, for which a written version exists, cf. no. 20 below.)
- Colloquium on Hopf algebras, quantum groups and tensor categories, Cordoba (Argentina) 31.8.-4.9.2009: Isocategorical compact groups


0. Die effektive Theorie für schwere Quarks und ihre Renormierung in Parameterdarstellung. (The effective theory of heavy quarks and its renormalization in parametric representation.) 91 pp. Unpublished diploma thesis in German. Technical University of Darmstadt, October 1992. (pdf)

1. Superselection structure of quantum field theories in 1+1 dimensions. 117pp. Doctoral dissertation. University of Hamburg, April 1997. DESY-preprint 97-073. (pdf)

2. Catégories tensorielles, algèbres et champs quantiques. Habilitation à diriger des recherches. Université Louis Pasteur Strasbourg, Decembre 2002. (pdf) (English version (pdf))

Journal papers

3. Quantum double actions on operator algebras and orbifold quantum field theories. Commun. Math. Phys. 181, 137-181 (1998) (hep-th/9606175) (pdf)

4. The superselection structure of massive quantum field theories in 1+1 dimensions. Rev. Math. Phys. 10, 1147-1170 (1998). (hep-th/9705019) (pdf)

5. On charged fields with group symmetry and degeneracies of Verlinde's matrix S. Ann. Inst. Henri Poincaré B (Phys. Théor.) 7, 359-394 (1999). (hep-th/9705018) (pdf)

6. On soliton automorphisms in massive and conformal theories. Rev. Math. Phys. 11, 337-359 (1999) (hep-th/9803057) (pdf)

7. Galois theory for braided tensor categories and the modular closure. Adv. Math. 150, 151-201 (2000). (math.CT/9812040) (pdf)

8. With Y. Kawahigashi and R. Longo: Multi-interval subfactors and modularity of representations in conformal field theory. Commun. Math. Phys. 219, 631-669 (2001) (math.OA/9903104) (pdf)

9. From subfactors to categories and topology I. Frobenius algebras in and Morita equivalence of tensor categories. J. Pure Appl. Alg. 180, 81-157 (2003) (math.CT/0111204) (pdf). This paper has been selected by Thomson-ISI, publisher of the Science Citation Index, as "Fast Breaking Paper" of the month April 2005 in the field of mathematics. Follow the preceding link or click here.

10. From subfactors to categories and topology II. The quantum double of tensor categories and subfactors. J. Pure Appl. Alg. 180, 159-219 (2003) (math.CT/0111205) (pdf)

11. On the structure of modular categories. Proc. Lond. Math. Soc. 87, 291-308 (2003) (math.CT/0201017) (pdf).

12. Galois extensions of braided tensor categories and braided crossed G-categories. J. Alg. 277, 256-281 (2004) (math.CT/0209093) (pdf)

13. On the center of a compact group. Intern. Math. Res. Notes. 2004:51, 2751-2756 (2004) (math.CT/0312257) (pdf)

14. With L. Tuset and J. E. Roberts: Representations of algebraic quantum groups and reconstruction theorems for tensor categories. Alg. Repres. Theor. 7, 517-573 (2004) (math.QA/0203206) (pdf)

15. Conformal orbifold theories and braided crossed G-categories. Commun. Math. Phys. 260, 727-762 (2005) (math.QA/0403322) (pdf). See also the erratum: Commun. Math. Phys. 260, 763 (2005) (pdf)

16. With L. Tuset: Monoids, embedding functors and quantum groups. Int. Journ. Math. 19, 1-31 (2008). (math-ph/0604065) (pdf)

17. Tensor categories: A selective guided tour. Revista de la Unión Matemática Argentina 51, 95-163 (2010). (arXiv:0804.3587) (pdf)

18. With A. Davydov, V. Ostrik and D. Nikshych: The Witt group of non-degenerate braided fusion categories. Journ. Reine Angew. Math. 677, 135-177 (2013). (arXiv:1009.2117).

19. A remark on the invariance of dimension. Mathem. Semesterberichte 62, 59-68 (2015). (arXiv:1310.8090) (pdf file)

20. On Karamata's proof of the Landau-Ingham Tauberian theorem. L'Enseign. Math. 61, 45-69 (2015). (arXiv:1311.2491) (pdf file)

21. On Ikehara type Tauberian theorems with O(x^\gamma) remainders. Abh. Math. Semin. Univer. Hamburg 88, 209-216 (2018). (arXiv:1612.01779)(pdf)

22. With L. Tuset: On the moments of a polynomial in one variable. Indag. Math. 31, 147-151 (2020). (open access).

23. With L. Tuset: The Mathieu conjecture for SU(2) reduced to an abelian conjecture. Indag. Math. 35, 114-118 (2024) (open access)

Papers in proceedings or other books

24. Disorder operators, quantum doubles, and Haag duality in 1+1 dimensions. In: Proceedings of the NATO Advanced Study Institute on "Quantum fields and quantum spacetime", Cargèse 1996. p. 349-356. Plenum Press, New York 1997. (hep-th/9611131)

25. Conformal field theory and Doplicher-Roberts reconstruction. In: R. Longo (ed.): "Mathematical physics in mathematics and physics. Quantum and operator algebraic aspects". Fields Inst. Commun. 30, 297-319 (2001). (math-ph/0008027) (pdf)

26. Abstract duality for symmetric tensor *-categories. (pdf) (Appendix to: Hans Halvorson: 'Algebraic Quantum Field Theory'.) In: J. Butterfield and J. Earman (eds.): "Handbook of the Philosophy of Physics", p. 865-922. North Holland, 2007. (math-ph/0602036) (pdf)

27. On Superselection theory of quantum fields in low dimensions (Invited lecture). p. 496-503 in: P. Exner (ed.): Proceedings of the XVIth International Congress on Mathematical Physics. (Prague, August 3-8, 2009.) World Scientific, 2010. (arXiv:0909.2537) (pdf)

28. On the structure of braided crossed G-categories. Appendix to V. Turaev: "Homotopy Quantum Field Theory". p. 221-235. European Mathematical Society, 2010. (pdf)

29. Modular categories. In: C. Heunen, M. Sadrzadeh, E. Grefenstette (eds.): Compositional methods in quantum physics and linguistics. Oxford University Press, 2013.. (arXiv:1201.6593)(pdf)


In preparation

30. Notes on the theorem of Baker-Campbell-Hausdorff-Dynkin. (pdf)

Reviews of my papers

Math Reviews and Zentralblatt MATH