  It is known that actions of field theories on a noncommutative space-time can
be written as some modified (we call them $\theta$-modified) classical actions
already on the commutative space-time (introducing a star product). Then the
quantization of such modified actions reproduces both space-time
noncommutativity and usual quantum mechanical features of the corresponding
field theory. The $\theta$-modification for arbitrary finite-dimensional
nonrelativistic system was proposed by Deriglazov (2003). In the present
article, we discuss the problem of constructing $\theta$-modified actions for
relativistic QM. We construct such actions for relativistic spinless and
spinning particles. The key idea is to extract $\theta$-modified actions of the
relativistic particles from path integral representations of the corresponding
noncommtative field theory propagators. We consider Klein-Gordon and Dirac
equations for the causal propagators in such theories. Then we construct for
the propagators path-integral representations. Effective actions in such
representations we treat as $\theta$-modified actions of the relativistic
particles. To confirm the interpretation, we quantize canonically these
actions. Thus, we obtain the Klein-Gordon and Dirac equations in the
noncommutative field theories. The $\theta$-modified action of the relativistic
spinning particle is just a generalization of the Berezin-Marinov
pseudoclassical action for the noncommutative case.
