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 hypothesiscan be viewed as adaptation of the classical Hamilton-Jacobi formalismto quantum mechanics. The construction reveals two key identities thatunderlie the formalism in Euclidean or Minkowski spaces. The first is a cocyclecondition, which is invariant underD-dimensional Möbius transformationswith Euclidean or Minkowski metrics. The second is a quadratic identity whichis a representation of theD-dimensional quantum Hamilton-Jacobi equation. In this approach, the solutions of the associated Schrödinger equation are usedto solve the nonlinear quantum Hamilton-Jacobi equation. A basic propertyof the construction is that the two solutions of the corresponding Schrödingerequation must be retained. The quantum potential, which arises in the formalism,can be interpreted as a curvature term. The author proposes that the quantumpotential, which is always nontrivial and is an intrinsic energy term characterisinga particle, can be interpreted as dark energy. Numerical estimates ofits magnitude show that it is extremely suppressed. In the multiparticle casethe quantum potential, as well as the mass, is cumulative.