Abstract. The BRST Charge plays a prominent role in interaction theory based on the Gauge symmetry group. In this work we find the explicit expression of the BRST charge for Generalized deformed SU(2) algebra.

The representation, à la Schwinger, of quantum algebra SU(3)pq is considered by constructing quantum commutation relations for p, q-deformed harmonic oscillators. The obtained results can be seen as a two-parameter extension of the quantum algebra SU(3)q studied in Ref. 1.

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The BRST Charge plays a prominent role in interaction theory based on the Gauge symmetry group. In this work we find the explicit expression of the BRST charge for Generalized deformed SU(2) algebra.

The deformed oscillators formalism plays a useful role in the study of physical models. Specifically, many variants of deformed oscillators have been used to study of the quantum optics, condensed matter physics, etc. .. In this paper we construct a (q, R)-deformed crystal lattice vibration for generic atomic string and calculate statistical distribution of this vibration. This is a fundament for study of crystal lattice vibration, which would give a base for a new quantization proceduce.