Abstract
The properties of the statistics in quantum mechanics (QM) and in quantum field theory (QFT) are reviewed from an algebraical point of view. It is indicated that the position and momentum operators in QM and fields in QFT are the `generators of finite-dimensional and infinite-dimensional orthosymplectic Lie superalgebras, respectively. The parastatistics corresponds to different representations of the same algebra. Examples of new possible statistics in QM and QFT with canonical variables generating sl( n) and (the central extension and completion of) sl ∞ are briefly discussed.
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