Geometry, Quantum Field Theory and NMR
We consider the nuclear magnetic resonance (NMR) problem of calculating the Carr-Purcell-Meiboom-Gill (CPMG) echo sequence for spins diffusing in a porous medium in a general magnetic field. We present explicit comparisons between the exact value of the echo sequence and the results predicted asymptotically at the boundaries of the space of parameters of the experiment. We also suggest an exponential term correction to the subleading “boundary” term in the short-time asymptotic formula, which is analogous to the exponential used in quantum field theoretic perturbation theory when going from connected to disconnected Feynman graphs. We discuss briefly how the results presented here answer questions that are analogous to basic questions in geometrical quantum field theory.
KeywordsFull Theory Asymptotic Regime Total Magnetization Differential Polynomial Background Magnetic Field
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