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It is known that actions of field theories on a noncommutative space-time canbe written as some modified (we call them $\theta$-modified) classical actionsalready on the commutative space-time (introducing a star product). Then thequantization of such modified actions reproduces both space-timenoncommutativity and usual quantum mechanical features of the correspondingfield theory. The $\theta$-modification for arbitrary finite-dimensionalnonrelativistic system was proposed by Deriglazov (2003). In the presentarticle, we discuss the problem of constructing $\theta$-modified actions forrelativistic QM. We construct such actions for relativistic spinless andspinning particles. The key idea is to extract $\theta$-modified actions of therelativistic particles from path integral representations of the correspondingnoncommtative field theory propagators. We consider Klein-Gordon and Diracequations for the causal propagators in such theories. Then we construct forthe propagators path-integral representations. Effective actions in suchrepresentations we treat as $\theta$-modified actions of the relativisticparticles. To confirm the interpretation, we quantize canonically theseactions. Thus, we obtain the Klein-Gordon and Dirac equations in thenoncommutative field theories. The $\theta$-modified action of the relativisticspinning particle is just a generalization of the Berezin-Marinovpseudoclassical action for the noncommutative case.

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action