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We discuss the imaginary-time formalism for field theories in thermalequilibrium in uniformly accelerating frames. We show that under a Wickrotation of Minkowski spacetime, the Rindler event horizon shrinks to a pointin a two-dimensional subspace tangential to the acceleration direction and theimaginary time. We demonstrate that the accelerated version of theKubo-Martin-Schwinger (KMS) condition implies an identification of allspacetime points related by integer-multiple rotations in the tangentialsubspace about this Euclidean Rindler event-horizon point, with the rotationalquanta defined by the thermal acceleration, $\alpha = a/T$. In the Wick-rotatedRindler hyperbolic coordinates, the KMS relations reduce to standard(anti-)periodic boundary conditions in terms of the imaginary proper time(rapidity) coordinate. Our findings pave the way to study, usingfirst-principle lattice simulations, the Hawking-Unruh radiation in geometrieswith event horizons, phase transitions in accelerating Early Universe, andearly stages of quark-gluon plasma created in relativistic heavy-ioncollisions.

Acceleration as a circular motion along an imaginary circle:  Kubo-Martin-Schwinger condition for accelerating field theories in  imaginary-time formalism