Petr Jizba, Fabio Scardigli
We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This interpretation leads to Feynman amplitudes that are in the Euclidean regime identical to transition probability of a Brownian particle propagating through a granular space. For illustration we consider the dynamics and the propagator of a Klein--Gordon particle. Implications for, doubly special relativity, quantum field theory and quantum gravity are discussed.
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http://arxiv.org/abs/1301.4091
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