Amplitude, phase, and complex analyticity

Abstract

Expressing the Schroedinger Lagrangian L in terms of the quantum wavefunction ψ = exp(S + iI) yields the conserved Noether current J = exp(2S)∇I. When ψ is a stationary state, the divergence of J vanishes. One can exchange S with I to obtain a new Lagrangian L and a new Noether current J = exp(2I)∇S, conserved under the equations of motion of L. However this new current J is generally not conserved under the equations of motion of the original Lagrangian L. We analyse the role played by J in the case when classical configuration space is a complex manifold, and relate its nonvanishing divergence to the inexistence of complex-analytic wavefunctions in the quantum theory described by L.

Boltzmann entropy of a Newtonian Universe

“…The notion that quantum mechanics is an emergent theory has been discussed at length in the literature [1,5,6,11,12,14,16]. Combined with the idea that spacetime as well is an emergent phenomenon [21,22,23,24,30], this paves the way for a computation of some thermodynamical properties of spacetime in quantum-mechanical terms.…”

Entropy, Topological Theories and Emergent Quantum Mechanics

“…[26] provides further evidence of the existing links between topological theories and quantum mechanics. Some of these links have been analysed in the present paper, from the alternative standpoint of the approach of emergence of quantum theory; further connections are being studied in an upcoming publication [28].…”