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            <title xml:lang="en">Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism</title>
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                <forename type="first">Victor E</forename>
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            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IDP">Institut Denis Poisson</idno>
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                    <forename type="first">Maxim N</forename>
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                <term xml:lang="en">rotation</term>
                <term xml:lang="en">space-time: Minkowski</term>
                <term xml:lang="en">quark gluon: plasma</term>
                <term xml:lang="en">heavy ion: scattering</term>
                <term xml:lang="en">dimension: 2</term>
                <term xml:lang="en">acceleration</term>
                <term xml:lang="en">Rindler</term>
                <term xml:lang="en">rapidity</term>
                <term xml:lang="en">circle</term>
                <term xml:lang="en">Euclidean</term>
                <term xml:lang="en">boundary condition</term>
                <term xml:lang="en">geometry</term>
                <term xml:lang="en">lattice</term>
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              <p>We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, $\alpha = a/T$. In the Wick-rotated Rindler 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, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe, and early stages of quark-gluon plasma created in relativistic heavy-ion collisions.</p>
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