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Removal of violations of the master Ward identity in perturbative QFT. (English) Zbl 1149.81017
One of the major obstacles in quantization is that symmetry properties of classical fields cannot easily be transferred to their quantum counterparts. This is mainly due to the fact that quantum fields are operator valued distributions. In perturbation theory one imposes Ward identities to maintain the corresponding conservations laws. In 2002 Dütsch and Boas proposed what they called the Master Ward Identity. Subsequently, this universal concept was studied in detail by Dütsch and Fredenhagen.
The present review is largely based on the diploma thesis of Brennecke (available as ps-file from DESY) written under the supervision of Fredenhagen. Traditionally, the Quantum Action Principle has been used to remove anomalies. In the present approach however, called causal perturbation theory, one works with interactions of compact support only and Planck’s constant is treated as a deformation parameter. The main advantage here is that quantum Yang-Mills theories can hopefully be studied in a curved spacetime background.

81T15 Perturbative methods of renormalization applied to problems in quantum field theory
70S10 Symmetries and conservation laws in mechanics of particles and systems
81T08 Constructive quantum field theory
81T50 Anomalies in quantum field theory
Full Text: DOI arXiv
[1] DOI: 10.1007/s00220-003-0968-4 · Zbl 1049.70017
[2] DOI: 10.1142/S0129055X02001454 · Zbl 1037.81074
[3] DOI: 10.1007/BF01907030 · Zbl 0221.35008
[4] DOI: 10.1103/PhysRevD.6.2145
[5] DOI: 10.1007/BF01609069
[6] DOI: 10.1007/BF01614158
[7] DOI: 10.1016/0003-4916(76)90156-1
[8] DOI: 10.1142/S0217732399001322
[9] Henneaux M., Quantization of Gauge Systems (1992) · Zbl 0838.53053
[10] Piguet O., Lect. Notes Phys. 28, in: Algebraic Renormalization: Perturbative Renormalization, Symmetries and Anomalies (1995)
[11] DOI: 10.1016/S0370-1573(00)00049-1 · Zbl 1097.81571
[12] DOI: 10.1007/s002200050004 · Zbl 1040.81067
[13] Dütsch M., Commun. Math. Phys. 203 pp 71–
[14] Dütsch M., Fields Inst. Commun. 30 pp 151–
[15] DOI: 10.1007/PL00005563 · Zbl 1019.81041
[16] DOI: 10.1142/S0129055X04002266 · Zbl 1084.81054
[17] Bogoliubov N. N., Introduction to the Theory of Quantized Fields (1959)
[18] Epstein H., Ann. Poincare Phys. Theor. A 19 pp 211–
[19] DOI: 10.1007/978-3-7643-7434-1_9
[20] DOI: 10.1098/rspa.1952.0158 · Zbl 0048.44606
[21] DOI: 10.1006/aphy.1994.1117 · Zbl 0806.58056
[22] Steinmann O., Lect. Notes Phys. 11, in: Perturbative Expansion in Axiomatic Field Theory (1971)
[23] DOI: 10.1007/978-3-662-04297-7
[24] Itzykson C., Quantum Field Theory (1980)
[25] DOI: 10.1007/BF02773492
[26] DOI: 10.1002/andp.200510145 · Zbl 1081.83011
[27] DOI: 10.1007/BF02750573
[28] DOI: 10.1103/PhysRev.84.350 · Zbl 0044.23301
[29] DOI: 10.1007/BF02831444
[30] DOI: 10.1142/S0129055X05002340 · Zbl 1078.81062
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