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This paper analytically investigates the interaction of light filaments generated by a femtosecond laser beam in air. It obtains the Hamiltonian of a total laser field and interaction force between two filaments with different phaseshifts and crcssing angles. The property of the interaction force, which leads the attraction or repulsion of filaments, isbasically dependent on the phase shift between filaments. The crossing angle between two filaments can only determinethe magnitude of the interaction force, but does not change the property of the force.