## $$q$$-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

### Keywords:

quantization; $$q$$-symmetry; field theory
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