Reaction rate in a heat bath

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We show in detail how the presence of a heat bath of photons effectively gives charged particles in the final state of a decay process a temperature-dependent mass, and changes the effective strength of the force responsible for the decay. At low temperature, gauge invariance causes both these effects to be largely cancelled by absorption of photons from the heat bath and by stimulated emission into it, but at high temperature the temperature-dependent mass is the dominant feature.