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Advances in High Energy Physics
Volume 2013 (2013), Article ID 957394, 10 pages
Research Article

The Equivalence Postulate of Quantum Mechanics, Dark Energy, and the Intrinsic Curvature of Elementary Particles

Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK

Received 9 April 2013; Accepted 23 April 2013

Academic Editor: Shi-Hai Dong

Copyright © 2013 Alon E. Faraggi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum mechanics. The construction reveals two key identities that underlie the formalism in Euclidean or Minkowski spaces. The first is a cocycle condition, which is invariant under -dimensional Möbius transformations with Euclidean or Minkowski metrics. The second is a quadratic identity which is a representation of the -dimensional quantum Hamilton-Jacobi equation. In this approach, the solutions of the associated Schrödinger equation are used to solve the nonlinear quantum Hamilton-Jacobi equation. A basic property of the construction is that the two solutions of the corresponding Schrödinger equation must be retained. The quantum potential, which arises in the formalism, can be interpreted as a curvature term. The author proposes that the quantum potential, which is always nontrivial and is an intrinsic energy term characterising a particle, can be interpreted as dark energy. Numerical estimates of its magnitude show that it is extremely suppressed. In the multiparticle case the quantum potential, as well as the mass, is cumulative.