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\(q\)-field theory. (English) Zbl 0831.58057
Summary: One may attempt to implement \(q\)-symmetry in field theory by replacing commutators by \(q\)-commutators. The quantized field is then described by \(q\)-oscillators. This program encounters a basic difficulty, however, when one demands either causality or consistency between the twin requirements of causality and positive energy. Independent of the preceding remark, one notes that the Einstein-Bose and Fermi-Dirac thermal distributions appear as limiting cases of the quantized \(q\)-field when \(q= \pm 1\).

MSC:
58Z05 Applications of global analysis to the sciences
81T70 Quantization in field theory; cohomological methods
53D50 Geometric quantization
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