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Foundations of Physics

, Volume 44, Issue 5, pp 512–522 | Cite as

Space-Time Grains: Roots of Special and Doubly Special Relativity

  • Petr Jizba
  • Fabio ScardigliEmail author
Article
  • 192 Downloads

Abstract

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. Some kind of spacetime granularity could be therefore held responsible for the emergence at larger scales of various symmetries. For illustration we consider also the dynamics and the propagator of a spinless relativistic particle. Implications for doubly special relativity, quantum field theory, quantum gravity and cosmology are discussed.

Keywords

Relativistic dynamics Superstatistics Path integrals Doubly special relativity 

Notes

Acknowledgements

The authors are grateful to H. Kleinert, Z. Haba, M. Sakellariadou, and L.S. Schulman for useful feedbacks.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.FNSPECzech Technical University in PraguePraha 1Czech Republic
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  3. 3.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan

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