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Majorana representation for dissipative spin systems

The Majorana representation of spin operators allows for efficient field-theoretical description of spin-spin correlation functions. Any N-point spin correlation function is equivalent to a 2N-point correlator of Majorana fermions. For a certain class of N-point spin correlation functions (including "auto" and "pair-wise" correlations) a further simplification is possible, as they can be reduced to N-point Majorana correlators. As a specific example we study the Bose-Kondo model. We develop a path-integral technique and obtain the spin relaxation rate from a saddle point solution of the theory. Furthermore, we show that fluctuations around the saddle point do not affect the correlation functions as long as the latter involve only a single spin projection. For illustration we calculate the 4-point spin correlation function corresponding to the noise of susceptibility.