  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.
