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

摘要

The equivalence postulate of quantum mechanics offers an axiomatic approachto quantum field theories and quantum gravity. The equivalence hypothesis canbe viewed as adaptation of the classical Hamilton-Jacobi formalism to quantummechanics. The construction reveals two key identities that underly theformalism in Euclidean or Minkowski spaces. The first is a cocycle condition,which is invariant under $D$--dimensional Mobius transformations with Euclideanor Minkowski metrics. The second is a quadratic identity which is arepresentation of the D-dimensional quantum Hamilton--Jacobi equation. In thisapproach, the solutions of the associated Schrodinger equation are used tosolve the nonlinear quantum Hamilton-Jacobi equation. A basic property of theconstruction is that the two solutions of the corresponding Schrodingerequation must be retained. The quantum potential, which arises in theformalism, can be interpreted as a curvature term. I propose that the quantumpotential, which is always non-trivial and is an intrinsic energy termcharacterising a particle, can be interpreted as dark energy. Numericalestimates of its magnitude show that it is extremely suppressed. In themulti--particle case the quantum potential, as well as the mass, arecumulative.