The inversion formula and 6j symbol for 3d fermions

In this work we study the 6j symbol of the 3d conformal group for fermionic operators. In particular, we study 4-point functions containing two fermions and two scalars and also those with four fermions. By using weight-shifting operators and harmonic analysis for the Euclidean conformal group, we relate these spinning 6j symbols to the simpler 6j symbol for four scalar operators. As one application we use these techniques to compute 3d mean field theory (MFT) OPE coefficients for fermionic operators. We then compute corrections to the MFT spectrum and couplings due to the inversion of a single operator, such as the stress tensor or a low-dimension scalar. These results are valid at finite spin and extend the perturbative large spin analysis to include non-perturbative effects in spin.

Quantum Mechanics-Based Structure Analysis of Cyclic Monoterpene Glycosides from Rhodiola Rosea

NMR- and MS-guided metabolomic mining for new phytoconstituents from a widely used dietary supplement, <i>Rhodiola rosea</i>, yielded two new (+)-myrtenol glycosides, <b>1</b> and <b>2</b>, and two new cuminol glycosides (<b>3</b> and <b>4</b>), along with three known analogues (<b>5</b>–<b>7</b>). The structures of the new compounds were determined by extensive spectroscopic analysis. Quantum Mechanics-driven ¹H iterative Full Spin Analysis (QM-HiFSA) decoded the spatial arrangement of the methyl groups in <b>1</b> and <b>2</b>, as well as other features not recognizable by conventional methods, including higher order spin-coupling effects. The application of QM-HiFSA will provide a definitive reference point for future phytochemical and biological studies of <i>R. rosea</i> as a resilience botanical. Application of a new NMR data analysis software package, CT, for QM-based iteration of NMR spectra is also discussed.

Quantum Mechanics-Based Structure Analysis of Cyclic Monoterpene Glycosides from Rhodiola Rosea

NMR- and MS-guided metabolomic mining for new phytoconstituents from a widely used dietary supplement, <i>Rhodiola rosea</i>, yielded two new (+)-myrtenol glycosides, <b>1</b> and <b>2</b>, and two new cuminol glycosides (<b>3</b> and <b>4</b>), along with three known analogues (<b>5</b>–<b>7</b>). The structures of the new compounds were determined by extensive spectroscopic analysis. Quantum Mechanics-driven ¹H iterative Full Spin Analysis (QM-HiFSA) decoded the spatial arrangement of the methyl groups in <b>1</b> and <b>2</b>, as well as other features not recognizable by conventional methods, including higher order spin-coupling effects. The application of QM-HiFSA will provide a definitive reference point for future phytochemical and biological studies of <i>R. rosea</i> as a resilience botanical. Application of a new NMR data analysis software package, CT, for QM-based iteration of NMR spectra is also discussed.