The geometrical underpinnings of a specific class of Dirac operators is discussed. It is demonstrated how this class of Dirac operators allow to relate various geometrical functionals like, for example, the Yang-Mills action and the functional of non-linear $σ-$models (i.e. of (Dirac) harmonic maps). These functionals are shown to be similar to the Einstein-Hilbert action with cosmological constant (EHC). The EHC may thus be regarded as a "generic functional". As a byproduct, the geometrical setup presented also allows to avoid the issue of "fermion doubling" as usually encountered, for instance, in the geometrical discussion of the Standard Model in terms of Dirac operators. Furthermore, it is demonstrated how the geometrical setup presented allows to derive the cosmological constant term of the EHC from the Einstein-Hilbert functional and the action of a purely gauge coupling Higgs field.
A dynamic correspondence between Bose-Einstein condensates and Friedmann-Lemaître-Robertson-Walker and Bianchi I cosmology with a cosmological constant
Brownian Motion in the Hilbert Space of Quantum States along with the Ricci Flow and Stochastically Emergent Einstein-Hilbert Action: Formulating a Well-Defined Feynman Path-Integral Measure for Quantum Fields in the Presence of Gravity
