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A stochastic model of a quantum field theory

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Abstract

The problem of obtaining a realistic relativistic description of a quantum system is discussed in the context of a simple (light-cone) lattice field theory. A natural stochastic model is proposed which, although nonlocal, is relativistic (in the appropriate lattice sense), and which is operationally indistinguishable from the standard quantum theory. The generalization to a broad class of lattice theories is briefly described.

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References

  1. J. S. Bell,Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987).

    Google Scholar 

  2. D. Bohm, A suggested interpretation of the quantum theory in terms of “hidden” variables I & II,Phys. Rev. 85:166–193 (1952).

    Google Scholar 

  3. J. S. Bell, Beables for quantum field theory, Preprint CERN-TH 4035/84 (1984) [reprinted in J. S. Bell,Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), pp. 173–180].

  4. S. M. Roy and V. Singh, Generalized beable quantum field theory,Phys. Lett. B 234: 117–120 (1990).

    Google Scholar 

  5. P. Pearle, Ways to describe state vector reduction,Phys. Rev. A 48:913–923 (1993).

    Google Scholar 

  6. I. C. Percival, Primary state diffusion,Proc. R. Soc. A 447:189–209 (1994).

    Google Scholar 

  7. J. F. Clauser and A. Shimony, Bell's theorem: Experimental tests and implications,Rep. Prog. Phys. 41:1881–1927 (1978).

    Google Scholar 

  8. D. Dürr, S. Goldstein, and N. Zhangí, On a realistic theory for quantum physics, inStochastic Processes, Physics and Geometry, S. Albeverioet al., eds. (World Scientific, Singapore, 1990), pp. 374–391.

    Google Scholar 

  9. K. S. Berndl, D. Dürr, S. Goldstein and N. Zhangí, Towards a relativistic quantum theory of particles (having trajectories), Talk at Third UK Conference on Foundations of Quantum Theory and Relativity, Cambridge (15 September 1994).

  10. K. S. Berndl and S. Goldstein, Comment on “Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories”,Phys. Rev. Lett. 72:780 (1994).

    Google Scholar 

  11. D. Dürr, S. Goldstein, and N. Zhangí, Quantum equilibrium and the origin of absolute uncertainty,J. Stat. Phys. 67:843–907 (1992).

    Google Scholar 

  12. G. C. Ghirardi, R. Grassi, and P. Pearle, Relativistic dynamical reduction models: General framework and examples,Found. Phys. 20:1271–1316 (1990).

    Google Scholar 

  13. C. Destri and H. J. de Vega, Light-cone lattice approach to fermionic theories in 2D,Nucl. Phys. B 290:363–391 (1987).

    Google Scholar 

  14. A. Fine, Joint distributions, quantum correlations, and commuting observables,J. Math. Phys. 23:1306–1310 (1982).

    Google Scholar 

  15. L. Hardy, Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories,Phys. Rev. Lett. 68:2981–284 (1992).

    Google Scholar 

  16. J. S. Bell, Quantum mechanics for cosmologists, inQuantum Gravity 2, C. Isham, R. Penrose, and D. Sciama, eds. (Clarendon Press, Oxford, 1981) [reprinted in J.S. Bell,Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), pp. 117–138].

    Google Scholar 

  17. A. Shimony, Events and processes in the quantum world, inQuantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Oxford University Press, Oxford, 1986), pp. 182–203.

    Google Scholar 

  18. J.S. Bell, Are there quantum jumps? inSchrödinger: Centenary Celebration of a Polymath, C. W. Kilmister, ed. (Cambridge University Press, Cambridge, 1987), pp. 41–52 [reprinted in J. S. Bell,Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), pp. 201–212].

    Google Scholar 

  19. N. Gisin, Stochastic quantum dynamics and relativity,Helv. Phys. Acta 62:363–371 (1989).

    Google Scholar 

  20. R. Haag, Fundamental irreversibility and the concept of events,Commun. Math. Phys. 132:245–251 (1990).

    Google Scholar 

  21. A. Kent, “Quantum jumps” and indistinguishability,Mod. Phys. Lett. 4:1834–1845 (1989).

    Google Scholar 

  22. R. P. Stanley,Enumerative Combinatorics (Wadsworth & Brooks/Cole Advanced Books, Monterey, California, 1986).

    Google Scholar 

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Samols, T.M. A stochastic model of a quantum field theory. J Stat Phys 80, 793–809 (1995). https://doi.org/10.1007/BF02178555

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