Some \(C^{\ast}\)-algebras associated to quantum gauge theories. (English) Zbl 1217.81126
Summary: 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.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 46L08 | \(C^*\)-modules |
| 18D10 | Monoidal, symmetric monoidal and braided categories (MSC2010) |
| 15A66 | Clifford algebras, spinors |
References:
| [1] | Wurzbacher, Infinite-Dimensional Kaehler Manifolds (2001) |
| [2] | DOI: 10.1007/s00220-004-1159-7 · Zbl 1078.58006 · doi:10.1007/s00220-004-1159-7 |
| [3] | DOI: 10.1017/CBO9780511564024 · Zbl 0964.81052 · doi:10.1017/CBO9780511564024 |
| [4] | DOI: 10.1142/S0129055X09003670 · Zbl 1183.81088 · doi:10.1142/S0129055X09003670 |
| [5] | Gracia-Bondia, Elements of Noncommutative Geometry (2001) · doi:10.1007/978-1-4612-0005-5 |
| [6] | Fredenhagen, Quantum Field Theory: Where We Are. Approaches to Fundamental Physics pp 61– (2007) |
| [7] | Epstein, Ann. Inst. H. Poincaré Sect. A (N.S.) 19 pp 211– (1973) |
| [8] | DOI: 10.1023/B:MATH.0000043318.42556.03 · Zbl 1079.43003 · doi:10.1023/B:MATH.0000043318.42556.03 |
| [9] | DOI: 10.1103/PhysRev.75.486 · Zbl 0032.23702 · doi:10.1103/PhysRev.75.486 |
| [10] | DOI: 10.1063/1.523318 · Zbl 0348.46056 · doi:10.1063/1.523318 |
| [11] | Dirac, Principles of Quantum Mechanics (1958) |
| [12] | Carey, Ann. Inst. H. Poincaré 40 pp 141– (1984) |
| [13] | DOI: 10.1007/s002200050499 · Zbl 0932.16038 · doi:10.1007/s002200050499 |
| [14] | DOI: 10.1007/BF02101555 · Zbl 0823.46064 · doi:10.1007/BF02101555 |
| [15] | DOI: 10.1007/s00220-005-1501-8 · Zbl 1115.46063 · doi:10.1007/s00220-005-1501-8 |
| [16] | DOI: 10.1063/1.531054 · Zbl 0847.17019 · doi:10.1063/1.531054 |
| [17] | DOI: 10.1007/s10468-009-9141-x · Zbl 1180.18002 · doi:10.1007/s10468-009-9141-x |
| [18] | Ashtekar, Knots and Quantum Gravity (1994) |
| [19] | Ashtekar, Lectures on Non-perturbative Canonical Gravity (1991) · doi:10.1142/1321 |
| [20] | Abramsky, Proceedings of the 19th IEEE Conference on Logic in Computer Science (LiCS’04) (2004) |
| [21] | DOI: 10.1142/S0129055X98000227 · Zbl 0917.46061 · doi:10.1142/S0129055X98000227 |
| [22] | DOI: 10.2307/1970397 · Zbl 0178.49301 · doi:10.2307/1970397 |
| [23] | Schwinger (ed.), Selected Papers on Quantum Electrodynamics (1958) · Zbl 0088.22203 |
| [24] | Schweber, QED and the Men Who Made it (1994) |
| [25] | Scharf, Finite Quantum Electrodynamics (1989) · Zbl 0844.53052 · doi:10.1007/978-3-662-01187-4 |
| [26] | Robinson, J. Lond. Math. Soc. (2) 49 pp 463– (1994) · Zbl 0840.15021 · doi:10.1112/jlms/49.3.463 |
| [27] | DOI: 10.1016/0001-8708(74)90068-1 · Zbl 0284.46040 · doi:10.1016/0001-8708(74)90068-1 |
| [28] | Plymen, Spinors in Hilbert Space (1994) |
| [29] | DOI: 10.1016/0022-1236(75)90004-X · Zbl 0295.46088 · doi:10.1016/0022-1236(75)90004-X |
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