Research interests and Publications, Graduate Students

Hendrik Grundling

Office:: Room 5104, Red Centre
Phone:: +61 2 9385 7104
Fax:: +61 2 9385 7123
Email:: H.Grundling@unsw.edu.au
Mail:

Brief History

B.Sc (Hons 1) University of Pretoria, 1976.

PhD University of Adelaide, 1986.

Postdoctoral Fellow, Mathematics, Australian National University, 1987-88.

School of Mathematics, UNSW, 1989-

Research Interests and Selected Papers

Mathematical Physics and C*-algebras, with particular emphasis on the following topics: Quantum Constraints, Quantum Field Theory, Quantum Gauge Theory, Quantization issues. Group Algebras for groups which are not locally compact.

Quantum Constraints

H. Grundling, C.A. Hurst: Algebraic Quantisation of Systems with a Gauge Degeneracy. Commun. Math. Phys. 98, 369-390 (1985) PDF version
H. Grundling, C.A. Hurst: Algebraic Structures of Degenerate Systems and the Indefinite Metric. J. Math. Phys. 28, 559-572 (1987) PDF version
H. Grundling: Systems with Outer Constraints. Gupta-Bleuler Electromagnetism as an Algebraic Field Theory. Commun. Math. Phys 114, 69-91 (1988) PDF version
H. Grundling, C.A. Hurst: A Note on Regular States and Supplementary Conditions. Lett. Math. Phys. 15, 205-212 (1988) PDF version Erratum Lett. Math. Phys. 17, 173-174 (1989) PDF version
H. Grundling, C.A. Hurst: The Quantum Theory of Second Class Constraints: Kinematics. Commun. Math. Phys. 119, 75-93 (1988) PDF version Erratum Commun. Math. Phys. 122, 527-529 (1989) PDF version
H. Grundling, C.A. Hurst: Constrained dynamics for quantum mechanics I. Restricting a particle to a surface. J. Math. Phys. 39, 3091-3119 (1998) PDF version
H. Grundling, F. Lledo, Local quantum constraints. Rev. Math. Phys. 12, 1159-1218 (2000). PDF version
H. Grundling: Quantum constraints. Rep. Math. Phys. 57, 97-120 (2006). PDF version
H. Grundling: BRST-Quantum theory: A functional analytic approach. Unpublished. A scanned version of the old preprint is here (11MB)

Quantum Gauge Theory

A. Carey, H. Grundling, I. Raeburn, C. Sutherland: Group Actions on C*-algebras, 3-cocycles and Quantum Field Theory. Commun. Math. Phys. 168, 389-416 (1995) PDF version
A. Carey, H. Grundling, C. Hurst, E. Langmann: Realizing 3-cocycles as Obstructions. J. Math. Phys. 36, 2605-2620 (1995) PDF version
A. Carey, H. Grundling, On the problem of the amenability of the gauge group. Lett. Math. Phys. 68, 113-120 (2004) PDF version
H. Baumgaertel, H. Grundling, Superselection in the presence of constraints. J. Math. Phys. 46,(8) 082303 (2005) PDF version
H. Grundling, G. Rudolph, QCD on an infinite lattice. (in print in Commun. Math. Phys.) PDF version

Other Quantum Field Theory Issues

H. Grundling, C.A. Hurst: The Operator Quantization of the Open Bosonic String: Field Algebra. Commun. Math. Phys. 156, 473-525 (1993) PDF version
D. Buchholz, H. Grundling: Algebraic supersymmetry: a case study. Comm. Math. Phys. 272, 699-750 (2007) PDF version
D. Buchholz, H. Grundling: The resolvent algebra: a new approach to canonical quantum systems. J. Funct. Anal. 254, (11) 2725-2779 (2008) PDF version
H. Grundling, K-H. Neeb: Localization via Automorphisms of the CARs. Local gauge invariance. Lett. Math. Phys. 93, 169-185 (2010) PDF version
D. Buchholz, H. Grundling: Lie Algebras of Derivations and Resolvent Algebras. (in print in Commun. Math. Phys.) PDF version

Quantization

M. Gotay, H. Grundling, C. Hurst: A Groenewald-Van Hove Theorem for S^2. Trans. Amer. Math. Soc. 348, 1579-1597 (1996) PDF version
M.J. Gotay, H. Grundling, G. Tuynman, Obstruction results in quantization theory. J. Nonlinear Sci. 6, 469-498 (1996) PDF version
M.J. Gotay, H. Grundling, On quantizing T*S^1. Rep. Math. Phys 40, 107-145 (1997) PDF version
M.J. Gotay, J. Grabowski, H. Grundling, An obstruction to quantizing compact symplectic manifolds, Proc. Amer. Math. Soc. 128, 237-243 (2000) PDF version
M.J. Gotay, H. Grundling, Nonexistence of finite-dimensional quantizations of a noncompact symplectic manifold, in: Differential geometry and applications (Brno, 1998), Masaryk University, Brno, 2000, 593-596. PDF version

Group C*-algebras for groups which are not locally compact

H. Grundling: A Group Algebra for Inductive Limit Groups: Continuity Problems of the Canonical Commutation Relations. Acta Applic. Math. 46, 107-145 (1997) PDF version
H. Grundling: Generalising group algebras. J. London Math. Soc. (2) 72,(3) 742-762 (2005) PDF version
Corrigendum. J. Lond. Math. Soc. (2) 77, 270-271 (2008) PDF version
(Whilst the existence and uniqueness theorem in the paper fails, it still provides an interesting setting for host algebras).
H. Grundling, K-H. Neeb: Full regularity for a C*-algebra of the Canonical Commutation Relations. Reviews Math. Phys. 21,(5) 787-613 (2009) PDF version
H. Grundling, K-H. Neeb: Infinite Tensor Products of C_0(R): Towards a Group Algebra for R^\infty. (in print in J. Op. Th.) PDF version
H. Grundling: Host Algebras. Unpublished. PDF version

Other.

H. Grundling, K-H. Neeb: Crossed Products of C*-algebras by Singular Actions. (Submitted) PDF version

H.Grundling: Integrated differential geometry. Commutative and noncommutative. Unpublished. PDF version

Graduate Students

Current and recent students:

Patrick Costello, The Mathematical Structure of the Quantum BRST-Constraint Method., PhD, 2002-2007. PDF version
Harry Ward, Dynamics Adjustment for Quantum Constraints, PhD, 2006-

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