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Particle production from the vacuum is a remarkable aspect of particlephysics. Prime examples are the Schwinger process of particle production instrong electric fields and the Hawking process of particle production fromblack holes. These processes can be viewed as quantum tunnelling of particlesfrom the vacuum. The tunnelling approach, and the closely related instanton orcomplex path approaches, are reviewed here with emphasis on paths in thecomplex coordinate plane. The method is applied to particle production from ablack hole in a magnetic field, where ultra-high energy charged particles areproduced.

Mining the quantum vacuum: quantum tunnelling and particle creation