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The general expression for the spin angular momentum is [1] =, where is the speed of light in free space and is the conjugate canonical momentum of the vector potential.The general expression for the orbital angular momentum of light is =, where = {,,,} denotes four indices of the spacetime and Einstein's summation convention has been applied.
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. [1] [2]: 183–184 Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
Left: "spin" angular momentum S is really orbital angular momentum of the object at every point. Right: extrinsic orbital angular momentum L about an axis. Top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω). [36] Bottom: momentum p and its radial position r from the axis. The total angular momentum ...
The total angular momentum of light consists of two components, both of which act in a different way on a massive colloidal particle inserted into the beam. The spin component causes the particle to spin around its axis, while the other component, known as orbital angular momentum (OAM), causes the particle to rotate around the axis of the beam.
The classical definition of angular momentum is =.The quantum-mechanical counterparts of these objects share the same relationship: = where r is the quantum position operator, p is the quantum momentum operator, × is cross product, and L is the orbital angular momentum operator.
The total angular momentum of a particle is the sum of both its orbital angular momentum and spin angular momentum. [3] A particle's spin is generally represented in terms of spin operators. It turns out for particles that make up ordinary matter (protons, neutrons, electrons, quarks, etc.) particles are of spin 1/2. [4] Only two energy levels ...
The angular momentum L in this equation may be the spin angular momentum, the orbital angular momentum, or the total angular momentum. The ratio between the true spin magnetic moment and that predicted by this model is a dimensionless factor g e , known as the electron g -factor : μ = g e ( − e ) 2 m e L . {\displaystyle {\boldsymbol {\mu ...
The orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and not on the polarization. OAM can be split into two types. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront.