The role of self-coherence in correlations of bosons and fermions in linear counting experiments. Notes on the wave-particle duality

Correlations of detection events in two detectors are studied in case of linear excitation of the measuring apparatus. On the basis of classical probability theory and fundamental conservation laws, a general formula is derived for the two-point correlation functions for both bosons and fermions. The results obtained coincide with that derivable from quantum theory which uses quantized field amplitudes. By applying both the particle and the wave picture at the same time, the phenomena of photon bunching and antibunching, photon anticorrelation and fermion antibunching, measured in beam experiments, are interpreted in the frame of an intuitively clear description.