Skip to main content Accessibility help
×
×
Home

SOME C*-ALGEBRAS ASSOCIATED TO QUANTUM GAUGE THEORIES

  • KEITH C. HANNABUSS (a1)

Abstract

Algebras associated with quantum electrodynamics and other gauge theories share some mathematical features with T-duality. Exploiting this different perspective and some category theory, the full algebra of fermions and bosons can be regarded as a braided Clifford algebra over a braided commutative boson algebra, sharing much of the structure of ordinary Clifford algebras.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      SOME C*-ALGEBRAS ASSOCIATED TO QUANTUM GAUGE THEORIES
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      SOME C*-ALGEBRAS ASSOCIATED TO QUANTUM GAUGE THEORIES
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      SOME C*-ALGEBRAS ASSOCIATED TO QUANTUM GAUGE THEORIES
      Available formats
      ×

Copyright

References

Hide All
[1]Abramsky, S. and Coecke, B., ‘A categorical semantics of quantum protocols’, Proceedings of the 19th IEEE Conference on Logic in Computer Science (LiCS’04) (IEEE Computer Society Press, Los Alamitos, CA, 2004).
[2]Ashtekar, A., Lectures on Non-perturbative Canonical Gravity (World Scientific, Singapore, 1991).
[3]Ashtekar, A. and Lewandowsi, J., ‘Representation theory of analytic holonomy C*-algebras’, in: Knots and Quantum Gravity, Oxford Lecture Series in Mathematics and its Applications, 1 (ed. Baez, J.) (Oxford University Press, New York, 1994).
[4]Beggs, E. and Majid, S., ‘Bar categories and star operations’, Algebr. Represent. Theory 12 (2009), 103152.
[5]Bouwknegt, P., Hannabuss, K. C. and Mathai, V., ‘Nonassociative tori and applications toT-duality’, Comm. Math. Phys. 264 (2006), 4169.
[6]Carey, A. L., ‘Lorentz invariant wave equations’, MSc dissertation, Oxford, 1973.
[7]Carey, A. L., ‘Inner automorphisms of hyperfinite factors and Bogoliubov transformations’, Ann. Inst. H. Poincaré 40 (1984), 141149.
[8]Carey, A. L., Gaffney, J. M. and Hurst, C. A., ‘A C*-algebra formulation of the quantization of the electromagnetic field’, J. Math. Phys. 18 (1977), 629640.
[9]Carey, A. L. and Grundling, H., ‘On the problem of the amenability of the gauge group’, Lett. Math. Phys. 68 (2004), 113120.
[10]Carey, A. L., Grundling, H., Hurst, C. A. and Langmann, E., ‘Realizing 3-cocycles as obstructions’, J. Math. Phys. 36 (1995), 26052620.
[11]Carey, A. L., Grundling, H., Raeburn, I. and Sutherland, C., ‘Group actions on C*-algebras, 3-cocycles and quantum field theory’, Comm. Math. Phys. 168 (1995), 389416.
[12]Connes, A. and Kreimer, D., ‘Hopf algebras, renormalization and noncommutative geometry’, Comm. Math. Phys. 199 (1998), 203242.
[13]Dirac, P. A. M., Principles of Quantum Mechanics, 4th edn (Clarendon Press, Oxford, 1958).
[14]Dyson, F., ‘The radiation theories of Tomonaga, Schwinger, and Feynman’, Phys. Rev. 75 (1949), 486502.
[15]Epstein, H. and Glaser, V., ‘The role of locality in perturbation theory’, Ann. Inst. H. Poincaré Sect. A (N.S.) 19 (1973), 211295.
[16]Fredenhagen, K., Rehren, K.-H. and Seiler, E., Quantum Field Theory: Where We Are. Approaches to Fundamental Physics, Lecture Notes in Physics, 721 (Springer, Berlin, 2007), pp. 6187.
[17]Gracia-Bondia, J. M., Varilly, J. C. and Figueroa, H., Elements of Noncommutative Geometry (Birkhäuser, Boston, 2001).
[18]Grundling, H. and Neeb, H., ‘Full regularity for a C *-algebra of the canonical commutation relations’, Rev. Math. Phys. 21 (2009), 587613.
[19]Kreimer, D., Knots and Feynman Diagrams, Cambridge Lecture Notes in Physics, 13 (Cambridge University Press, Cambridge, 2000).
[20]Mathai, V. and Rosenberg, J., ‘T-duality for torus bundles with H-fluxes via noncommutative geometry’, Comm. Math. Phys. 253 (2005), 705721.
[21]Plymen, R. and Robinson, P. L., Spinors in Hilbert Space, Cambridge Tracts in Mathematics, 114 (Cambridge University Press, Cambridge, 1994).
[22]Rieffel, M. A., ‘Induced representations of C*-algebras’, Adv. Math. 13 (1974), 176257.
[23]Robinson, P. L., ‘Modular theory and Bogoliubov autmomorphisms of Clifford algebras’, J. Lond. Math. Soc. (2) 49 (1994), 463476.
[24]Scharf, G., Finite Quantum Electrodynamics (Springer, Berlin, 1989).
[25]Schweber, S. S., QED and the Men Who Made it (Princeton University Press, Princeton, NJ, 1994).
[26]Schwinger (ed.), J., Selected Papers on Quantum Electrodynamics (Dover Publications, New York, 1958).
[27]Selinger, P., ‘Dagger compact closed categories and completely positive maps’, Proceedings of the 3rd International Workshop on Quantum Programming Languages, Chicago, June 30–July 1, 2005.
[28]Shale, D. and Stinespring, W. F., ‘States of the Clifford algebra’, Ann. of Math. (2) 80 (1964), 365381.
[29]Spera, M. and Wurzbacher, T., ‘Determinants, Pfaffians and quasi-free representations of the CAR algebra’, Rev. Math. Phys. 10 (1998), 705721.
[30]Takai, H., ‘On a duality for crossed products of C *-algebras’, J. Funct. Anal. 19 (1975), 2539.
[31]Wurzbacher, T., ‘Fermionic second quantization and the geometry of the restricted Grassmannian’, in: Infinite-Dimensional Kaehler Manifolds, Birkhäuser Series on DMV-Seminars, 31 (eds. Huckleberry, A. and Wurzbacher, T.) (Birkhäuser, Basel, 2001).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed