Manuscript X-A-ST@1 · X-A-ST.tex · section · d9ccbde1

Switch, ramp, and gauge algebra

Frozen classical prescription › Switch, ramp, and gauge algebra · lines 560–577

X-A-ST@1#eq:metriclaw, X-A-ST@1#eq:scalarlaw

For scalars put $X_{ξ} = ξ^{μ} \partial_{μ}$ ; for scalar densities put $D_{ξ} r = \partial_{μ} (ξ^{μ} r)$ . The full coefficient transformations are

h^{'} k^{'} ϕ_{0}^{'} ϕ_{2}^{'} = h + K ξ, = k + L_{ξ} h + K ζ + \frac{1}{2} L_{ξ}^{2} η, = ϕ_{0}, ϕ_{1}^{'} = ϕ_{1} + X_{ξ} ϕ_{0}, = ϕ_{2} + X_{ξ} ϕ_{1} + X_{ζ} ϕ_{0} + \frac{1}{2} X_{ξ}^{2} ϕ_{0} .

Deleting the quadratic terms in (eq:metriclaw) would change the problem.

Displayed formulas in this passage

X-A-ST@1#eq:metriclaw · line 565
$h^{'} k^{'} ϕ_{0}^{'} ϕ_{2}^{'} = h + K ξ, = k + L_{ξ} h + K ζ + \frac{1}{2} L_{ξ}^{2} η, = ϕ_{0}, ϕ_{1}^{'} = ϕ_{1} + X_{ξ} ϕ_{0}, = ϕ_{2} + X_{ξ} ϕ_{1} + X_{ζ} ϕ_{0} + \frac{1}{2} X_{ξ}^{2} ϕ_{0} .$
X-A-ST@1#eq:scalarlaw · line 565
$h^{'} k^{'} ϕ_{0}^{'} ϕ_{2}^{'} = h + K ξ, = k + L_{ξ} h + K ζ + \frac{1}{2} L_{ξ}^{2} η, = ϕ_{0}, ϕ_{1}^{'} = ϕ_{1} + X_{ξ} ϕ_{0}, = ϕ_{2} + X_{ξ} ϕ_{1} + X_{ζ} ϕ_{0} + \frac{1}{2} X_{ξ}^{2} ϕ_{0} .$