Journal Articles | Book Chapters | Conference Papers | Books Edited


  1. Holonomy and the Wess-Zumino term", (A.L. Carey, M.K. Murray), Letters in Math Physics, (1986), 323-328
  2. "Temperature states on loop groups, theta functions and the Luttinger model", (A.L. Carey, K.C. Hannabuss), J Func Analysis, 75 (1987) , 128-160
  3. "Current algebras, gauge groups and Kac-Moody algebras", (A.L. Carey, S.N.M. Ruijsenaars),Acta Math Applicandae (1987), 1-81
  4. "On an automorphic action of U(n,1) on On", (A.L. Carey, D.E. Evans), J Func Analysis, 70 (1987), 90-110
  5. "Operator algebras of the two dimensional Ising model", (A.L. Carey, D.E. Evans), Proc Santa Cruz Conf on Artin's braid group, Amer Math Soc Co ntemporary Mathematical series 78 (1988), 117-166
  6. "Infinite complex spin groups", (A.L. Carey, J. Palmer), J Func Analysis, 83 (1989), 1-43
  7. "Gauge anomalies on S2 and group extensions", (A.L. Carey, J. Palmer), J Math Phys., 30 (1989), 2181-2191
  8. "Degenerate forms of Maxwell's equations", (A.L. Carey, K. McNamara), J Aust Math Soc., B (1989)
  9. "Algebras almost commuting with Clifford Algebras", (A.L. Carey, D.E. Evans), J Func Analysis, 88 (1990), 279-298.
  10. "Clifford algebras, Riemann surfaces and infinite dimensional groups", (A.L. Carey, M.G. Eastwood and K.C. Hannabuss), Commun Math Phys., 13 0 (1990), 213-236
  11. "L2-acyclicity and L2-torsion invariants", (A.L. Carey, V. Mathai), Amer Math Soc Contemporary Math Series , 105 (1990), 91-118
  12. "Simple examples of conformal field theories",(A.L. Carey, K.C. Hannabuss), Int J Mod Physics, B4 (1990), 1059-1068
  13. "Higher order tensors, strings and newtensors", (A.L. Carey, M.K. Murray), Proc Royal Soc, 430 (1990), 423-432
  14. "Non-monomial representations of nilpotent groups II", (L. Baggett, A.L. Carey, W. Moran and A. Ramsey), J Func Analysis, (1991) 361-372
  15. "The Pompieu problem for groups", (A.L. Carey, E. Kaniuth, W. Moran), Proc Camb Phil Soc, 109 (1991) 45-58
  16. "String structures and holonomy", (A.L. Carey, M.K. Murray), Commun Math Phys, 141 (1991), 441-452
  17. "Algebras almost commuting with Clifford algebras in a IIinf factor", (A.L. Carey, J. Phillips), K-theory, 4 (1991) 445-478
  18. "Temperature states on gauge groups", (A.L. Carey, K.C. Hannabuss), Annales d'Institut Henri Poincare, B57 (1992) 219-257
  19. "Return to Equilibrium in the presence of Phase Transitions", (A.L. Carey, L. Hume), J Stat Phys, 68 (1992) 787-827
  20. "L2-torsion invariants", (A.L. Carey, V.Mathai), (40) J Func Analysis, 110 (1992) 377-408
  21. "Finite dimensional algebraic representations of the basic phylon group", (O.E. Bandorff-Nielson, P. Blaesid, A.L. Carey, P.E. Jupp, M. Mora, M.K. Mu rray), Acta Applicandae Math, 28 (1992) 219-252
  22. "Hilbert space represenations of the gauge groups of some two dimensional field theories", (A.L. Carey, J.D. Wright), Reviews in Math Phys, 5 (1993), 25-47
  23. "Landau Lifshitz equation, elliptic curves and the Ward transform", (A.L. Carey, K.C. Hannabuss, L. Mason, M.A. Singer), Commun Math Phys, 154 (1993) 551-586
  24. "Kirillov theory for divisible nilpotent groups", (A.L. Carey, W. Moran and C.E.M. Pearce), Math Annalen, 301 (1995) 119-133
  25. "Cohomology of group actions on C*-algebras, 3-cocycles and quantum field theory", (A.L. Carey, H. Grundling, I. Raeburn, C. Sutherland), Commun M ath Phys, 168 (1995) 389-416
  26. "A general existence theorem for orthonormal wavelets", (L. Baggett, A.L. Carey, W. Moran, P. Ohring), Publ RIMS, Kyoto 31 (1995) 95-111
  27. "Realising 3-cocycles as obstructions", (A.L. Carey, H. Grundling, C.A> Hurst, E. Langmann), J Math Phys, 36 (1995), 2605-2621
  28. "Infinite dimensional groups and Riemann surface field theories." (A.L. Carey, K.C. Hannabuss), Commun Math Phys, 176 (1996), 321-351
  29. "Faddeev's anomaly and bundle gerbes", (A.L. Carey, M.K. Murray), Letters in Math Phys, 37(1) (1996) 29-36
  30. "A discrete model of the quantum Hall effect", (A.L. Carey, P. McCann), Publ RIMS 32 (1996), 117-156
  31. "Higher bundle gerbes, descent equations and 3-cocycles", (A.L. Carey, M.K. Murray, B. Wang), J Geom Phys, 21 (1997) 183-197
  32. "Von Neumann spectral invariants near the spectral gap", (A.L. Carey, T. Coulhon, V. Mathai, J. Phillips), Bull Math Sci France, 122 (1 998) 203-242
  33. "Quantum groups at odd roots of unity and topological invariants of 3-manifolds", (R.B. Zhang, A.L. Carey), Commun math Phys, 182 (1996) 619-636
  34. "Index theory, gerbes and Hamiltonian quantisation," (A.L.Carey, J. Mickelsson and M.K. Murray) Commun. Math. Phys. 183, 707-723 (1997)
  35. " Seiberg-Witten monopoles in three dimensions," (B.L. Wang, A.L.Carey, R.B. Zhang and J. McCarthy) Lett. Math. Phys. 39, 213-228 (1997)
  36. " Determinant lines and L2-torsion ," (A.L.Carey M. Farber and V. Mathai) J. reine angew. Math 48, 153-181 (1997)
  37. "The spherical phylon group and invariants of the Laplace transform," (A.L.Carey, M.G.Eastwood, P.E.Jupp, M.K.Murray) ) Proc Roy Soc Lond 454, 1255-1268 (1998)
  38. "The quantum Hall effect on the hyperbolic plane," (A.L.Carey, K. C. Hannabuss, V. Mathai and P.J. McCann) Commun. Math. Phys. 190, 629-673 (1998)
  39. " Unbounded Fredholm modules and spectral flow," (A.L.Carey and J. Phillips) J. Canadian Math. Soc. 50, 673-718 (1998)
  40. "Principal bundles and the Dixmier-Douady class," (A.L.Carey, D. Crowley and M.K. Murray) Commun. Math. Phys. 193, 171-196 (1998)
  41. "Loop Groups, Anyons and the Calogero-Sutherland model," (A.L.Carey, E. Langmann) Commun. Math. Phys. 201, 1-34 (1999)
  42. "The quantum hall effect on the hyperbolic plane in the presence of disorder," (A.L.Carey, K. C. Hannabuss and V. Mathai) Lett. Math. Phys. 47, 215-236 (1999)
  43. "Bundle gerbes applied to quantum field theory," (A.L.Carey, J. Mickelsson and M. K. Murray) Rev. Math. Phys. 12, 65-90 (2000)
  44. "Correspondences, von Neumann algebras and holomorphic $L^2$ torsion," (A.L.Carey, M. Farber and V. Mathai) Canadian Journal of Mathematics 52, 695-736 (2000)
  45. "On unbounded p-summable Fredholm modules," (A.L.Carey, J. Phillips and F. A. Sukochev) Advances in Math 151, 140-163 (2000)
  46. "Cuntz algebras and quantum groups," (A.L.Carey, A. Paolucci and R.B. Zhang) Annales Henri Poincare 1, 1097-1122 (2000)
  47. "A gerbe obstruction to quantisation of fermions on odd-dimensional manifolds with boundary," (A.L.Carey and J. Mickelsson) Lett. Math. Phys. 51, 145-160 (2000)
  48. "A gerbe obstruction to quantisation of fermions on odd-dimensional manifolds with boundary," (A.L.Carey and J. Mickelsson) Lett. Math. Phys. 51, 145-160 (2000)
  49. "Hilbert C*-systems for actions of the circle group," (H. Baumgaertal and A.L.Carey) Reports. Math. Phys. 47, 47-60 (2001)
  50. "The Universal Gerbe, Dixmier-Douady classes and gauge theory," (A.L.Carey and J. Mickelsson) Lett. Math. Phys. 59, 47-60 (2002)
  51. "K-theory of bundle gerbes and twisted K-theory", (A.L. Carey, P. Bouwknegt, V.Mathai, M.K.Murray and D. Stevenson) Commun Math Phys, 228 (2002) 17-49 (hep-th 0106194)
  52. "Spectral flow and Dixmier traces", (A.L. Carey, J. Phillips and F. Sukochev) Advances in Mathematics, 173 (2003) 68-113
  53. "The geometric triangle for 3-dimensional Seiberg-Witten monopoles", (A.L. Carey, M. Marcolli, B-L. Wang) Communications in Contemporary Mathematics, 5 (2003) 197-250
  54. "Seiberg-Witten-Floer homology and gluing formulae'' (A.L. Carey and B-L. Wang) Acta Academia Sinica, 19 (2003), 245-296.
  55. "Spectral flow in Fredholm modules, eta invariants and the JLO cocycle'', (A.L. Carey and J. Phillips) K-Theory 31 (2004) 135-194.
  56. "The Hochschild Class of the Chern Character for Semifinite Spectral Triples", (A.L. Carey, J. Phillips, A. Rennie, F.A. Sukochev) Journal of Functional Analysis 213 (2004), pp 111-153
  57. "Holonomy on D-Branes", (A.L. Carey, S. Johnson and M.K. Murray) J. Geom. Phys. 52 (2004) 186-215
  58. "On the amenability of the gauge group", (A.L. Carey, H. Grundling) Lett. Math. Phys. 68 (2004),113--120
  59. "L2 torsion without the Determinant class condition and extended $L^2$ cohomology", (M. Braverman, A.L. Carey, V. Mathai and M. Farber.) Commun. Cont. Math.. 7, (2005), 421-462
  60. "The local index formula in semifinite von Neumann algebras I: spectral flow", (A.L. Carey, J. Phillips, A. Rennie, F.A. Sukochev) Advances in Math , 202, (2006), 451-516
  61. "The local index formula in semifinite von Neumann algebras II; even case.", (A.L. Carey, J. Phillips, A. Rennie, F.A. Sukochev) Advances in Math , 202, (2006), 517-554
  62. "Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories", (A.L.Carey, S.Johnson, M.K. Murray, D. Stevenson, B-L. Wang) Commun Math Phys 259 (2005) 577-613.
  63. "On the relationship of gerbes to the odd families index theorem", (A.L. Carey, B.L. Wang) J. Geom. Phys., 57 (2006) 23-38
  64. "Dixmier traces and some applications in noncommutative geometry", (A.L. Carey, F. A. Sukochev) Russian Mathematical Surveys., 61 (2006) 1039-1100
  65. "Quantum Hall effect and noncommutative geometry", (A.L. Carey, K.C. Hannabuss and V. Mathai) J. Geometry and Symmetry in Physics, 6,(2006) 16-37
  66. "Thom Isomorphism and push-forward map in twisted K-theory" (with B-L. Wang) Journal K Theory, 1 (2008) 357-393
  67. "Operator integrals, spectral flow and the spectral shift function" (with N. A. Azamov, P.G. Dodds, F.A. Sukochev) Canadian J Math, 61, (2009) 241-263
  68. "Asymptotics of zeta functions and Dixmier traces" (with A.A. Sedaev, F.A Sukochev and A. Rennie) J. Funct. Analysis 249 (2007) 253-283
  69. "The Spectral shift function and spectral flow" (with N. A. Azamov, and F.A. Sukochev) Commun. Math. Phys. 276 (2007) 51-91.
  70. "Fusion of Symmetric D-branes and Verlinde Rings" (with B-L. Wang) Commun. Math. Phys. 277 (2008) 577-625.
  71. "The Chern Character of Semifinite Spectral Triples" (with J. Phillips, A. Rennie, F.A. Sukochev) Journal of Noncommutative Geometry 2 (2008) 141-261.
  72. "Differential Twisted K-theory and Twisted eta forms", (with J. Mickelsson and Bai-ling Wang), J. Geom and Physics, 59, (2009), 632-653.
  73. "Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators" (with F. A. Sukochev and D. Potapov), Advances in Mathematics 222 (2009) 1809-1849.
  74. "Bivariant cyclic theory and the families index theorem," with M-T Benameur, Electronic Research Announcements in Mathematical Sciences (ERA-MS) 16 (2009) 37-43
  75. "Modular index theory of $SU(2)_q$", (with A. Rennie and K. Tong) J. Geom Phys. 59 (2009) 1431-1452
  76. "APS Boundary Conditions, $KK$-theory and Spectral Flow in Graph C*-Algebras" (with J.Phillips and A. Rennie), J. reine angew. Math. 643 (2010) 59-109.
  77. "Twisted cyclic theory and an index theory for the gauge invariant KMS state on the Cuntz algebras" (with J. Phillips and A. Rennie). Journal K Theory, 6} (2010), 339-380
  78. "Twisted cyclic theory, equivariant $KK$-theory and KMS states" (with R. Nest, S. Neshveyev and A. Rennie) J. reine angew. Math. 651 (2011) 161-191.
  79. "A Dirac Type Operator on the Non-Commutative Disk" (with S. Klimek and K. P. Wojciechowski) Letters in Mathematical Physics 93, 107-125, 2010
  80. "Riemann-Roch and index formulae in twisted K-theory" (with B-L Wang) Symposia in Pure Mathematics, 81 (2010) 95-131, American Mathematical Society, Providence RI.
  81. " Families of type III KMS states on a class of C*-algebras containing O_n and Q_N", (with J. Phillips, I Putnam, A. Rennie), J. Funct. Analysis, 260 (2011) 1637-1681.
  82. " Integration on locally compact noncommutative spaces" (with V. Gayral, A. Rennie, F. Sukochev) J. Funct Analysis, 263 (2012) 383-414.
  83. " Measurable operators and the asymptotics of heat kernels and zeta functions", (with F. Sukochev) J. Funct. Analysis, 262 (2012) 4582-4599.
  84. " Higher spectral flow and an entire bivariant JLO cocycle," (with M-T Benameur) J. K Theory, 11, (2013) 183-232.
  85. "K-cycles for twisted K-homology," {with P. Baum and B-L Wang} J. K Theory}, 12, (2013) 69-98


  1. "Index theory for locally compact noncommutative geometries," (with V. Gayral, A. Rennie, F. Sukochev) Memoirs of the Amer. Math. Soc. 231, No 1085, 2014


  1. "The infinite dimensional spin and complex orthogonal groups and applications", Operator Algebras and Applications, London Math Soc Lecture Notes S eries, 135 (1988), 77-102
  2. "Phylon representations", (A.L. Carey, P. Jupp, M.K. Murray), in Australian Mathematical Society Lecture Series, "Algebraic Groups and Related Subjects; a Volume in Honour of R. W. Richardson", (Eds: G.I. Lehrer with A.L. Carey, T. Carroll, M.K. Murray, T. Springer), Cambridge University Press, 1996
  3. "Loop Groups and Quantum Field Theory", (with E. Langmann), Birkhauser, to appear.
  4. "Analytic formulae for Spectral Flow in von Neumann algebras" (M.T. Benameur, A.L. Carey, J. Phillips, A. Rennie, F.A. Sukochev, K.P. Wojciechowski) "Analysis, Geometry and topology of elliptic operators." eds B. Booss-Bavnbek, S.Klimek, M. Lesch, W. Zhang, World Scientific, Singapore, 2006
  5. "Spectral Triples: examples and applications" (with John Phillips and Adam Rennie) European Mathematical Society Lectures in Mathematics and Physics, Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory, European Mathematical Society, Zurich, 2011.


  1. "Bundle gerbes and field theory", (A.L. Carey, J. Mickelsson and M.K. Murray), Proceedings of the International Congress of Mathematical Physics 1997 (1999)
  2. "Loop groups, Luttinger model, Anyons and Sutherland systems", International Workshop, "Mathematical Physics" at the occasion of W. Thirring's 70th birthday, 12-17 May 1997, Kiev, Ukraine; Ukrainian Journal of Physics 6-7 vol. 43, 817-827 (1998), (A.L. Carey and E. Langmann)
  3. "Torsion, current algebra and Hamiltonian quantisation", (A.L. Carey, J. Mickelsson and M.K. Murray), Proc 2nd International Workshop on Lie theory an d its applications in physics, (eds: H.D. Doebner, V.V. Dobrev and J. Hilgert), World Scientific, Singapore (1999), 204-209
  4. "Hamiltonian quantization of fermions on an odd dimensional manifold with boundary." (A.L. Carey and J. Mickelsson), Proceedings of the Goslar confere nce (International Symposium on Quantum Theory and Symmetries, July 1999), World Scientific
  5. "Notes on the Seiberg-Witten theory", (A.L. Carey and B. Wang), Contemporary Math, 258 71-86, 2000
  6. "Group actions on Cuntz algebras", (with D.E. Evans), Proc Centre for Math Anaglysis IX, Miniconference on linear analysis and functi on spaces, (1985).
  7. "Representions of infinite dimnesional groups and applications", Proc Centre for Math Analysis, ANU, Miniconference on Harmonic Analysis and Operat or Algebras, 16 (1988)
  8. "Non-monomial representations of abelian groups with multipliers", (with L.W. Baggett, W. Moran and A. Ramsay), Proc Centre for Math Analysis, ANU, 15 (1987), 1-5
  9. "L2 Reidermeister-Franz torsion", (with V. Mathai), Proc Centre for math Analysis, ANU, Conference on Geometry and Physics, (1989)
  10. "Loop Groups and Quantum Field Theory" (with E. Langmann) in Geometric Analysis and Applications to Quantum Field Theory, P Bouwknegt and S Wu (editors), Progress in Mathematics Vol 205, pp 45-94 Birkhauser, Boston, 2002
  11. "Some examples of odd index theorems" Reports in Mathematical Physics, 57 (2006) 41-51
  12. "Semifinite Spectral triples associated to graph $C^*$-algebras" (with John Phillips and Adam Rennie),"Traces in Geometry, Number Theory and Quantum Fields" Sergio Albeverio, Matilde Marcolli, Sylvie Paycha, Jorge Plazas (Editors) Aspects of Mathematics 38, 35-56, Vieweg Verlag 2008.
  13. "The Local Index Formula in Noncommutative Geometry Revisited" (with John Phillips, Adam Rennie and Fedor A Sukochev) Noncommutative Geometry and Physics 3, pp 3-36, World Scientific, Singapore, 2013.
  14. "Semi-Finite Noncommutative Geometry and Some Applications" (with John Phillips and Adam Rennie) Noncommutative Geometry and Physics 3, pp 37-58, World Scientific, Singapore 2013.
  15. "Recent Advances in the Study of the Equivariant Brauer Group" (with Peter Bouwknegt and Rishni Ratnam) Noncommutative Geometry and Physics 3, pp 335-358, World Scientific, Singapore 2013.


  1. "Confronting the Infinite", (Eds: A.L. Carey, W. Ellis, P.A. Pearce, A.W. Thomas), World Scientific, 1995
  2. Australian Mathematical Society Lecture Series, "Algebraic groups and Related Subjects: a Volum in Honour of R. W. Richardson", (Eds: G.I. Lehrer with A.L. Carey, T. Carroll, M.K. Murray, T. Springer), Cambridge University Press, 1996
  3. Australian Mathematical Society Lecture Series, "Geometric analysis and lie theory in Mathematics and Physics" (Eds: A.L. Carey and M.K. Murray), Cambridge University Press, 1998
  4. Clay Mathematics Proceedings, Vol 12, "Motives, Quantum Field Theory and Pseudodifferential Operators", (Eds: Alan Carey. David Ellwood, Sylvie Paycha, Steven Rosenberg), American Mathematical Society, Providence RI, 2010
  5. European Mathematical Society Lectures in Mathematics and Physics, "Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory", 2011.