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The rotation of a photon around an axis with orientation given by the vector n⃗ is the action representated by the operator $ U = e^{ i \theta \vec{n}. \vec{J} } $. But to get a clearer understanding of what that would mean in a specific case... $$ $$ Suppose $ \vec{n} $ were parallel to $ \vec{J} $ and that and the photon's direction of propagation is along z and that at time $t = t_0$, the photon's electric field $ \vec{E} $ were pointing up along y direction. Suppose now at $t_0$, the photon is 'rotated' about $ \vec{n} $ by an angle $ \Pi $, (180 degrees) what now are the directions of $ \vec{E} $ and $ \vec{J} $ ?

The rotation of a photon around an axis with orientation given by the vector n⃗ is the action representated by the operator $ U = e^{ i \theta \vec{n}. \vec{J} } $. But to get a clearer understanding of what that would mean in a specific case... $$ $$ Suppose $ \vec{n} $ were parallel to $ \vec{J} $ and that and the photon's direction of propagation is along $z$ and that at time $t = t_0$, the photon's electric field $ \vec{E} $ were pointing up along $y$ direction. $$ $$ Suppose now at $t_0$, the photon is 'rotated' about $ \vec{n} $ by an angle $ \Pi $, (180 degrees) what now are the directions of $ \vec{E} $ and $ \vec{J} $ ?

The rotation of a photon around an axis with orientation given by the vector n⃗ is the action representated by the operator $ U = e^{ i \theta \vec{n}. \vec{J} } $. But to get a clearer understanding of what that would mean in a specific case... $$ $$ Suppose $ \vec{n} $ were parallel to $ \vec{J} $ and that and the photon's direction of propagation is along z and that at time t = t0, the photon's electric field $ \vec{E} $ were pointing up along y direction. Suppose now at t0, the photon is 'rotated' about $ \vec{n} $ by an angle $ \Pi $, (180 degrees) what now are the directions of $ \vec{E} $ and $ \vec{J} $ ?

The rotation of a photon around an axis with orientation given by the vector n⃗ is the action representated by the operator $ U = e^{ i \theta \vec{n}. \vec{J} } $. But to get a clearer understanding of what that would mean in a specific case... $$ $$ Suppose $ \vec{n} $ were parallel to $ \vec{J} $ and that and the photon's direction of propagation is along z and that at time $t = t_0$, the photon's electric field $ \vec{E} $ were pointing up along y direction. Suppose now at $t_0$, the photon is 'rotated' about $ \vec{n} $ by an angle $ \Pi $, (180 degrees) what now are the directions of $ \vec{E} $ and $ \vec{J} $ ?

The rotation of a photon around an axis with orientation given by the vector $\vec n$ is the action representated by the operator $$U=\exp(iθ\vec n\cdot\vec J).$$

But to get a clearer understanding of what that would mean in a specific case:

Suppose $\vec{n}$ were parallel to $\vec{J}$ and that and the photons direction of propagation were along the $z$ axis, and that at time $t = t_0$ the photon's electric field $\vec{E}$ was pointing up along the $y$ direction. Now suppose that at $t_0$ the photon is 'rotated' about $\vec{n}$ by an angle $\pi$ ($180^\circ$). What are the directions of $\vec{E}$ and $\vec{J}$ now?

The rotation of a photon around an axis with orientation given by the vector n⃗ is the action representated by the operator $ U = e^{ i \theta \vec{n}. \vec{J} } $. But to get a clearer understanding of what that would mean in a specific case... $$ $$ Suppose $ \vec{n} $ were parallel to $ \vec{J} $ and that and the photon's direction of propagation is along z and that at time t = t0, the photon's electric field $ \vec{E} $ were pointing up along y direction. Suppose now at t0, the photon is 'rotated' about $ \vec{n} $ by an angle $ \Pi $, (180 degrees) what now are the directions of $ \vec{E} $ and $ \vec{J} $ ?