Equivalence principle, higher-dimensional Möbius group and the hidden antisymmetric tensor of quantum mechanics

We show that the recently formulated equivalence principle (EP) implies a basic cocycle condition both in Euclidean and Minkowski spaces, which holds in any dimension. This condition, that in one dimension is sufficient to fix the Schwarzian equation, implies a fundamental higher-dimensional Mobius invariance which, in turn, unequivocally fixes the quantum version of the Hamilton-Jacobi equation. This also holds in the relativistic case, so that we obtain both the time-dependent Schrodinger equation and the Klein-Gordon equation in any dimension. We then show that the EP implies that masses are related by maps induced by the coordinate transformations connecting different physical systems. Furthermore, we show that the minimal coupling prescription, and therefore gauge invariance, arises quite naturally in implementing the EP. Finally, we show that there is an antisymmetric 2-tensor which underlies quantum mechanics and sheds new light on the nature of the quantum Hamilton-Jacobi equation.

[1]  G. Jaeger.  Bohmian Mechanics and Quantum Theory , 2000 .

[2]  I. Vancea,et al.  Duality between coordinates and Dirac field , 2000, hep-th/0002217.

[3]  I. Vancea,et al.  Duality of Coordinates and Matter Fields in Curved Spacetime , 1999, gr-qc/9907059.

[4]  S. Goldstein,et al.  Bohmian Mechanics and Quantum Theory , 2000 .

[5]  David Marcus Appleby,et al.  Bohmian Trajectories Post-Decoherence , 1999, quant-ph/9908029.

[6]  E. Floyd,et al.  Classical Limit of the Trajectory Representation of Quantum Mechanics and Residual Indeterminacy , 1999 .

[7]  David Marcus Appleby,et al.  Generic Bohmian Trajectories of an Isolated Particle , 1999, quant-ph/9905003.

[8]  R. Carroll.  Some remarks on time, uncertainty, and spin , 1999, quant-ph/9903081.

[9]  A. Faraggi,et al.  THE EQUIVALENCE POSTULATE OF QUANTUM MECHANICS , 1998, hep-th/9809127.

[10]  A. Faraggi,et al.  Equivalence principle: tunnelling, quantized spectra and trajectories from the quantum HJ equation , 1998, hep-th/9809126.

[11]  A. Faraggi,et al.  Equivalence Principle, Planck Length and Quantum Hamilton-Jacobi Equation , 1998, hep-th/9809125.

[12]  I. Vancea.  Gravity and duality between coordinates and matter fields , 1998, gr-qc/9801072.

[13]  A. Faraggi,et al.  Quantum Transformations , 1998, hep-th/9801033.

[14]  A. Faraggi,et al.  The Equivalence principle of quantum mechanics: Uniqueness theorem , 1997, hep-th/9711028.

[15]  E. Floyd,et al.  WHICH CAUSALITY? DIFFERENCES BETWEEN TRAJECTORY AND COPENHAGEN ANALYSES OF AN IMPULSIVE PERTURBATION , 1997, quant-ph/9708026.

[16]  E. Floyd.  REFLECTION TIME AND THE GOOS-HÄNCHEN EFFECT FOR REFLECTION BY A SEMI-INFINITE RECTANGULAR BARRIER , 1997, quant-ph/9708007.

[17]  R. Carroll.  (X, ψ) duality and enhanced dKdV on a Riemann surface , 1997, hep-th/9705229.

[18]  A. Faraggi,et al.  Quantum mechanics from an equivalence principle , 1997, hep-th/9705108.

[19]  G. Ghirardi,et al.  Bohmian Mechanics Revisited , 1997, quant-ph/9704021.

[20]  E. Floyd,et al.  Where and why the generalized Hamilton-Jacobi representation describes microstates of the Schrödinger wave function , 1996, quant-ph/9707051.

[21]  E. Floyd.  The Ermakov invariant for the trajectory representation of quantum mechanics , 1996 .

[22]  James T. Cushing,et al.  Bohmian mechanics and quantum theory: an appraisal , 1996 .

[23]  M. Matone.  Instantons and recursion relations in N = 2 SUSY gauge theory☆ , 1995, hep-th/9506102.

[24]  K. Berndl,et al.  On the global existence of Bohmian mechanics , 1995, quant-ph/9503013.

[25]  L. Susskind.  The world as a hologram , 1994, hep-th/9409089.

[26]  C. R. Stephens,et al.  Black hole evaporation without information loss , 1993, gr-qc/9310006.

[27]  P. Holland.  The de Broglie-Bohm theory of motion and quantum field theory , 1993 .

[28]  P. Holland.  The Quantum Theory of Motion , 1993 .

[29]  Matti Vuorinen,et al.  Conformal Geometry and Quasiregular Mappings , 1988 .

[30]  E. Floyd,et al.  Progress in a trajectory interpretation of the Klein-Gordon equation , 1988 .

[31]  Floyd.  Closed-form solutions for the modified potential. , 1986, Physical Review D, Particles and fields.

[32]  E. Floyd.  Arbitrary initial conditions of nonlocal hidden variables , 1984 .

[33]  E. Floyd.  Modified potential and Bohm's quantum-mechanical potential , 1982 .

[34]  E. Floyd.  Bohr-Sommerfeld quantization with the effective action variable , 1982 .

[35]  L. Ryder,et al.  Quantum Field Theory , 2001, Foundations of Modern Physics.

[36]  D. Bohm.  A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .