Exotic Probability Theories and Quantum Mechanics: References

Dear Friends,

I thought that it might be useful to collect references relevant to exotic probability theories and their relation to quantum mechanics. If you see something missing, please let me know as I would like to keep this up to date (I know that Carlos Rodriguez of SUNY Albany has papers in preparation).

If you are new to this subject, there is no comprehensive review or introduction, but you might want to look at my talk from the 1995 Bayesian conference to get an idea of what this is all about.

Regards,

Saul Youssef

  1. A.V. Belinskii, How could you measure a negative probability?, JETP letters, 59, 301 (1994).
  1. D.J.Miller, Realism and Time Symmetry in Quantum Mechanics, Phys. Lett. A 1996.
  1. Ariel Caticha, Consistency and Linearity in Quantum Theory, Phys.Rev. A57, 1572 (1998).
  2. Ariel Caticha, Consistency, Amplitudes and Probabilities in Quantum Theory, preprint, 1998.
  1. Richard Feynman, Negative Probabilities, in Quantum Implications, eds B.J. Hiley and F.David Peat (Routledge and Kegan Paul, 1987).
  1. F.H.Frohner, The Riesz-Fejer Theorem: Missing Link between Probability Theory and Quantum Mechanics, Forschungszentrum Karlsruhe, FZKA 5888, May, 1997.
  2. F.H.Frohner, Quantum Mechanics - How Weird for Bayesians?, in Maximum Entropy and Bayesian Methods, ed. A.Mohammad-Djafari and G. Demoments, Kluwer Academic Publishers, (1993).
  1. Stanley Gudder, A theory of amplitudes, J.Math.Phys. 29, 9 (1988).
  2. Stanley Gudder, Realism in Quantum Mechanics, Found. Phys. 19, 949 (1989).
  3. Stanley Gudder, A new formulation of quantum mechanics, Int. Journ.Theor.Phys. 31(1992) 15.
  4. Stanley Gudder, Realistic Spin, Found. Phys. Vol 22, 1 (1992).
  1. Andrew Khrennikov, p-adic probability distributions of hidden variables, SFB 237 Preprint 257, 1995.
  2. Andrew Khrennikov, p-adic probability interpretation of Bell's inequality, Phy. Lett. A 200(1995).
  1. W.Muckenheim et al., Phys. Rep. 133, 339 (1983). (An interesting review.)
  2. W.Muckenheim, On quasi-realistic local spin models and extended probabilities, Phys. Lett. A 175(1993).
  1. Itamar Pitowsky, Resolution of the Einstein-Podolsky-Rosen and Bell Paradoxes, Phys.Rev.Lett. 48, 1299 (1982).
  2. Itamar Pitowsky, Deterministic model of spin and statistics, Phys. Rev. D27, 2316 (1983).
  1. Slater, P.B. "Quantum Coin-Tossing in a Bayesian Jeffreys Framework", Phys. Lett. A 206 (1995).
  1. Aephraim Steinberg, How Much Time Does a Tunneling Particle Spend in the Barrier Region? Phys.Rev.Lett. 13, 2405 (1995).
  2. Aephraim Steinberg, Conditional Probabilities in Quantum Theory and the Tunneling Time Controversy Phys.Rev. A52, 32 (1996).
  1. S.K.Srinivasan and E.C.G. Sudarshan, Complex measures and amplitudes, generalized stochastic processes and their application to quantum mechanics., J.Phys. A. Math Gen. 27 (1994).
  2. S.K. Srinivasan, Quantum Mechanics via Extended Measures, J.Phys.A (23) 8297, (1997).
  3. S.K. Srinivasan, Complex Masure, Coherent State and Squeezed State Representation, J.Phys.A(?)
  4. S.K. Srinivasan, Complex Measureable Processes and Path Integrals, preprint.
  1. Y. Tikochinsky, Feynman Rules for Probability Amplitudes, Int.J.Theor.Phys., 27, 543 (1988).
  2. Y.Tikochinsky, On the generalized multiplication and addition of complex numbers, J.Math.Phys. 29 (1988).
  1. Saul Youssef, A Reformulation of Quantum Mechanics, Mod.Phys.Lett. A6, 225-236 (1991).
  2. Saul Youssef, Quantum Mechanics as Complex Probability Theory, Mod.Phys.Lett A9, 2571 (1994).
  3. Saul Youssef, Is Quantum Mechanics an Exotic Probability Theory?, in Fundamental Problems in Quantum Theory; Conference in Honor of Professor John A. Wheeler, ed: D.M. Greenberger and A. Zeilinger, Annals of the New York Academy of Sciences, Volume 755, April, 1995.
  4. Saul Youssef, Quantum Mechanics as an Exotic Probability Theory, proceedings of the Fifteenth International Workshop on Maximum Entropy and Bayesian Methods, ed. K.M.Hanson and R.N.Silver, Santa Fe, August, 1995.
  5. Saul Youssef, Is Complex Probability Theory Consistent with Bell's Theorem?, Phys.Lett. A204, 181(1995).
If you know of more papers related to this subject, please let me know.