Bibliography

ABS

M. F. Atiyah, R. Bott and A. Shapiro, ``Clifford modules'', Topology 3 (1964), 3-38.

BHMS

P. Baum, P. M. Hajac, R. Matthes and W. Szymanski, ``Noncommutative geometry approach to principal and associated bundles'', Warszawa, 2006, forthcoming.

BGV

N. Berline, E. Getzler and M. Vergne, Heat Kernels and Dirac Operators, Springer, Berlin, 1992.

Bla

B. Blackadar, $K$-theory for Operator Algebras, 2nd edition, Cambridge Univ. Press, Cambridge, 1998.

Bost

J.-B. Bost, ``Principe d'Oka, $K$-théorie et systèmes dynamiques non commutatifs'', Invent. Math. 101 (1990), 261-333.

BR

O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 1, Springer, New York, 1987.

BT

P. Budinich and A. Trautman, The Spinorial Chessboard, Trieste Notes in Physics, Springer, Berlin, 1988.

BW

H. Bursztyn and S. Waldmann, ``Bimodule deformations, Picard groups and contravariant connections'', K-Theory 31 (2004), 1-37.

CPRS

A. L. Carey, J. Phillips, A. Rennie and F. A. Sukochev, ``The Hochschild class of the Chern character for semifinite spectral triples'', J. Funct. Anal. 213 (2004), 111-153.

Che

C. Chevalley, The Algebraic Theory of Spinors, Columbia Univ. Press, New York, 1954.

Con1

A. Connes, ``The action functional in noncommutative geometry'', Commun. Math. Phys. 117 (1988), 673-683.

Con

A. Connes, Noncommutative Geometry, Academic Press, London and San Diego, 1994.

Con2

A. Connes, ``Gravity coupled with matter and foundation of noncommutative geometry'', Commun. Math. Phys. 182 (1996), 155-176.

CDV

A. Connes and M. Dubois-Violette, ``Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples'', Commun. Math. Phys. 230 (2002), 539-579.

CL

A. Connes and G. Landi, ``Noncommutative manifolds, the instanton algebra and isospectral deformations'', Commun. Math. Phys. 221 (2001), 141-159.

CM

A. Connes and H. Moscovici, ``The local index formula in noncommutative geometry'', Geom. Func. Anal. 5 (1995), 174-243.

DLSSV

L. Dabrowski, G. Landi, A. Sitarz, W. van Suijlekom and J. C. Várilly, ``The Dirac operator on $SU_q(2)$'', Commun. Math. Phys. 259 (2005), 729-759.

DS

L. Dabrowski and A. Sitarz, ``Dirac operator on the standard Podles quantum sphere'', in Noncommutative Geometry and Quantum Groups, P. M. Hajac and W. Pusz, eds. (Instytut Matematyczny PAN, Warszawa, 2003), pp. 49-58.

Dix

J. Dixmier, Les $C^*$-algèbres et leurs Représentations, Gauthier-Villars, Paris, 1964; 2nd edition, 1969.

Dix1

J. Dixmier, ``Existence de traces non normales'', C. R. Acad. Sci. Paris 262A (1966), 1107-1108.

Fri

T. Friedrich, Dirac Operators in Riemannian Geometry, Graduate Studies in Mathematics 25, American Mathematical Society, Providence, RI, 2000.

GGISV

V. Gayral, J. M. Gracia-Bondía, B. Iochum, T. Schücker and J. C. Várilly, ``Moyal planes are spectral triples'', Commun. Math. Phys. 246 (2004), 569-623.

GV

J. M. Gracia-Bondía and J. C. Várilly, ``Algebras of distributions suitable for phase-space quantum mechanics. I'', J. Math. Phys. 29 (1988), 869-879.

GVF

J. M. Gracia-Bondía, J. C. Várilly and H. Figueroa, Elements of Noncommutative Geometry, Birkhäuser, Boston, 2001.

HH

J. W. Helton and R. E. Howe, ``Integral operators: traces, index, and homology'', in Proceedings of a Conference on Operator Theory, P. A. Fillmore, ed., Lecture Notes in Mathematics 345, Springer, Berlin, 1973; pp. 141-209.

Hig

N. Higson, ``The local index formula in noncommutative geometry'', in Contemporary Developments in Algebraic K-Theory, M. Karoubi, A. O. Kuku and C. Pedrini, eds. (ICTP, Trieste, 2004), pp. 443-536. Also available at the URL <http://www.math.psu.edu/higson/Papers/trieste.pdf>

Kar

G. Karrer, ``Einführung von Spinoren auf Riemannschen Mannigfaltigkeiten'', Ann. Acad. Sci. Fennicae Ser. A I Math. 336/5 (1963), 3-16.

LM

H. B. Lawson and M.-L. Michelsohn, Spin Geometry, Princeton Univ. Press, Princeton, NJ, 1989.

Lich

A. Lichnerowicz, ``Spineurs harmoniques'', C. R. Acad. Sci. Paris 257A (1963), 7-9.

LSS

S. Lord, A. A. Sedaev and F. A. Sukochev, ``Dixmier traces as singular symmetric functionals and applications to measurable operators'', J. Funct. Anal. 224 (2005), 72-106.

Mil

J. W. Milnor, Morse Theory, Princeton University Press, Princeton, NJ, 1963.

Moy

J. E. Moyal, ``Quantum mechanics as a statistical theory'', Proc. Cambridge Philos. Soc. 45 (1949), 99-124.

Ply

R. J. Plymen, ``Strong Morita equivalence, spinors and symplectic spinors'', J. Oper. Theory 16 (1986), 305-324.

RW

I. Raeburn and D. P. Williams, Morita Equivalence and Continuous-Trace $C^*$-algebras, Amer. Math. Soc., Providence, RI, 1998.

RS

M. Reed and B. Simon, Methods of Modern Mathematical Physics, I: Functional Analysis, Academic Press, New York, 1972.

Ren

A. Rennie, ``Smoothness and locality for nonunital spectral triples'', $K$-Theory 28 (2003), 127-165.

Rie

M. A. Rieffel, Deformation Quantization for Actions of $\bR^d$, Memoirs of the American Mathematical Society 506, Providence, RI, 1993.

Schd

H. Schröder, ``On the definition of geometric Dirac operators'', Dortmund, 2000; math.dg/0005239.

Sch1

E. Schrödinger, ``Diracsches Elektron in Schwerefeld I'', Sitzungsber. Preuss. Akad. Wissen. Phys.-Math. 11 (1932), 105-128.

Schz

L. Schwartz, Théorie des Distributions, Hermann, Paris, 1966.

Schw

L. B. Schweitzer, ``A short proof that $M_n(A)$ is local if $A$ is local and Fréchet'', Int. J. Math. 3 (1992), 581-589.

See

R. T. Seeley, ``Complex powers of an elliptic operator'', Proc. Symp. Pure Math. 10 (1967), 288-307.

Sim

B. Simon, Trace Ideals and their Applications, Cambridge Univ. Press, Cambridge, 1979.

SDLSV

W. van Suijlekom, L. Dabrowski, G. Landi, A. Sitarz and J. C. Várilly, ``The local index formula for $SU_q(2)$'', K-Theory (2006), in press.

Tay

M. E. Taylor, Partial Differential Equations II, Springer, Berlin, 1996.

VG

J. C. Várilly and J. M. Gracia-Bondía, ``Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra'', J. Math. Phys. 29 (1988), 880-887.

Wodz

M. Wodzicki, ``Local invariants of spectral asymmetry'', Invent. Math. 75 (1984), 143-178.

Wolf

J. A. Wolf, ``Essential selfadjointness for the Dirac operator and its square'', Indiana Univ. Math. J. 22 (1973), 611-640.