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Equation 6 · Part 1 · Every Crystal Has Its Own Speed of Light

Symbol A_x

∥[Ax(t),By]∥≤C e−(d(x,y)−cLR t)/ξ\lVert [A_x(t), B_y] \rVert \le C\, e^{-\left(d(x,y) - c_{\mathrm{LR}}\, t\right)/\xi}
AxA_x

What this part means

the bound says that for two operators.

Its job in the formula

AxA_x is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

Stated formally, the bound says that for two operators AxA_x and ByB_y acting on well-separated lattice sites x and y , the size of their commutator after evolving one of them forward in time t is capped by an exponential in the distance between the sites minus the cone’s own reach: ∥[Ax(t),By]∥≤C e−(d(x,y)−cLR t)/ξ\lVert [A_x(t), B_y] \rVert \le C\, e^{-\left(d(x,y) - c_{\mathrm{LR}}\, t\right)/\xi}.

The passage around this formula

Stated formally, the bound says that for two operators AxA_x and ByB_y acting on well-separated lattice sites x and y , the size of their commutator after evolving one of them forward in time t is capped by an exponential in the distance between the sites minus the cone’s own reach: ∥[Ax(t),By]∥≤C e−(d(x,y)−cLR t)/ξ\lVert [A_x(t), B_y] \rVert \le C\, e^{-\left(d(x,y) - c_{\mathrm{LR}}\, t\right)/\xi}. where C and ξ\xi are constants fixed by the…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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