By means of the Schwinger variational principle, we show that a field theory with a linearly realized symmetry admits the generalized g-statistics as a possible solution.
Defalco, L., Mignani, R., Scipioni, R. (1995). VARIATIONAL APPROACH TO GENERALIZED STATISTICS. NUOVO CIMENTO DELLA SOCIETÀ ITALIANA DI FISICA. A, NUCLEI, PARTICLES AND FIELDS, 108(2), 263-266.