Manuscript XX-E@1 · XX-E.tex · section · cf7a8f40

A declared comparison counterterm family

Explicit Newton-contact images and comparison Ward images › A declared comparison counterterm family · lines 1019–1043

XX-E@1#eq:RT, XX-E@1#eq:Ccandidate

Let $T$ be a fixed local linear differential map with smooth coefficients whose output is a uniformly compact spatial vector source on compact time intervals. Define

(R_{T} z)^{a} = - G_{sp} \partial_{i} (T z)^{ia} .

Let $m (z, w)$ be a symmetric local bilinear differential expression with smooth coefficients. Set

C_{m, T; f} (z) = \frac{s ^{2}}{2} \int f (m (z, z) - 2 R_{T} z \cdot \nabla ℓ z) d t d^{3} x .

This is a specified comparison family of insertion corrections. If used with an overall factor $ℏ$ , it does not change the classical symbol.

Displayed formulas in this passage

XX-E@1#eq:RT · line 1025
$(R_{T} z)^{a} = - G_{sp} \partial_{i} (T z)^{ia} .$
XX-E@1#eq:Ccandidate · line 1033
$C_{m, T; f} (z) = \frac{s ^{2}}{2} \int f (m (z, z) - 2 R_{T} z \cdot \nabla ℓ z) d t d^{3} x .$

A declared comparison counterterm family

Displayed formulas in this passage

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