| Summary: | A solution of the Dirac equation in a strong laser field presenting a nonspreading wave packet in the rest frame of the electron is derived. It consists of a generalization of the self-accelerating free electron wavepacket [I. Kaminer et al., Nat. Phys. 11, 261 (2015)1745-247310.1038/nphys3196] to the case with the background of a strong laser field. Built upon the notion of nonspreading for an extended relativistic wavepacket, the concept of Born rigidity for accelerated motion in relativity is the key ingredient of the solution. At its core, the solution comes from the connection between the self-accelerated free electron wavepacket and the eigenstate of a Dirac electron in a constant and homogeneous gravitational field via the equivalence principle. The solution is an essential step towards the realization of the laser-driven relativistic collider [S. Meuren et al., Phys. Rev. Lett. 114, 143201 (2015)0031-900710.1103/PhysRevLett.114.143201], where the large spreading of a common Gaussian wavepacket during the excursion in a strong laser field strongly limits the expectable yields.
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