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Related Concept Videos

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
¹H NMR Signal Multiplicity: Splitting Patterns01:13

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When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.

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Setting Limits on Supersymmetry Using Simplified Models
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Maximal-helicity-violating n-point one-loop amplitude in N=4 supergravity.

David C Dunbar1, James H Ettle, Warren B Perkins

  • 1College of Science, Swansea University, Swansea, United Kingdom.

Physical Review Letters
|March 10, 2012
PubMed
Summary
This summary is machine-generated.

We present a new formula for calculating amplitudes in N=4 supergravity theories. This formula simplifies complex calculations using soft and collinear factorizations.

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Area of Science:

  • Theoretical physics
  • Quantum field theory
  • String theory

Background:

  • N=4 supergravity is a highly symmetric quantum field theory with applications in diverse areas of physics.
  • Calculating scattering amplitudes in these theories is crucial for understanding fundamental interactions.
  • Maximal-helicity-violating (MHV) amplitudes are a special class of amplitudes that exhibit significant simplification.

Purpose of the Study:

  • To derive an explicit formula for the n-point maximal-helicity-violating (MHV) one-loop amplitude in N=4 supergravity.
  • To provide a computationally tractable method for evaluating these amplitudes.

Main Methods:

  • Utilizing the principles of soft and collinear factorization.
  • Applying these factorization properties to the structure of one-loop amplitudes.

Main Results:

  • An explicit, closed-form formula for the n-point MHV one-loop amplitude in N=4 supergravity has been derived.
  • The formula is shown to be consistent with known results and provides a systematic way to compute these amplitudes.

Conclusions:

  • The derived formula offers a significant advancement in the calculation of scattering amplitudes in N=4 supergravity.
  • This work potentially opens new avenues for exploring the structure and properties of maximally supersymmetric gauge and gravity theories.