From Molecular Quantum Electrodynamics at Finite Temperatures to Nuclear Magnetic Resonance

Abstract: The algebraic reformulation of molecular Quantum Electrodynamics (mQED) at finite temperatures is applied to Nuclear Magnetic Resonance (NMR) in order to provide a foundation for the reconstruction of much more detailed molecular structures, than possible with current methods. Conventional NMR theories are based on the effective spin model which idealizes nuclei as fixed point particles in a lattice $L$, while molecular vibrations, bond rotations and proton exchange cause a delocalization of nuclei. Hence, a lot information on molecular structures remain hidden in experimental NMR data, if the effective spin model is used for the investigation. In this document it is shown how the quantum mechanical probability density $\mid\Psi^\beta(X)\mid^2$ on $\mathbb{R}^{3n}$ for the continuous, spatial distribution of $n$ nuclei can be reconstructed from NMR data. To this end, it is shown how NMR spectra can be calculated directly from mQED at finite temperatures without involving the effective description. The fundamental problem of performing numerical calculations with the infinite-dimensional radiation field is solved by using a purified representation of a KMS state on a $W^*$-dynamical system. Furthermore, it is shown that the presented method corrects wrong predictions of the effective spin model. It is outlined that the presented method can be applied to any molecular system whose electronic ground state can be calculated using a common quantum chemical method. Therefore, the presented method may replace the effective spin model which forms the basis for NMR theory since 1950.