Manuscript I-B-VP@3 · I-B-VP-v3.tex · section · 93c04eb4

Scale-invariant irregular extensions

Scale-invariant irregular extensions · lines 2054–2080

For example, mode $0$ gives

F_{E_{0}^{(0)}} = \frac{α ^{- 2} [ 1 + 6 β ( 1 + β )] - 1}{48 π ^{2} r ^{2}},

j_{φ, E_{0}^{(0)}} = - \frac{e β ( 1 + β ) ( 1 + 2 β )}{12 π ^{2} α ^{2} r ^{2}},

and (eq:T-complex) with

P = α^{- 2} [1 + 6 β (1 + β)] - 1, C = α^{- 4} [1 - 30 β^{2} (1 + β)^{2}] - 1.

At $ξ = 1/6$ ,

δ T^{μ}_{ν} = - \frac{∣ q ∣ ^{3}}{6 π ^{2} α ^{4} r ^{4}} diag (1, 1, - 3, 1) .

As $β \to 0^{+}$ , the mode- $0$ correction vanishes. Under charge conjugation the mode- $0$ choice at $β$ is exchanged with mode $- 1$ at $1 - β$ , and the current changes sign.

Displayed formulas in this passage

unlabeled · line 2057
$F_{E_{0}^{(0)}} = \frac{α ^{- 2} [ 1 + 6 β ( 1 + β )] - 1}{48 π ^{2} r ^{2}},$
unlabeled · line 2061
$j_{φ, E_{0}^{(0)}} = - \frac{e β ( 1 + β ) ( 1 + 2 β )}{12 π ^{2} α ^{2} r ^{2}},$
unlabeled · line 2067
$P = α^{- 2} [1 + 6 β (1 + β)] - 1, C = α^{- 4} [1 - 30 β^{2} (1 + β)^{2}] - 1.$
unlabeled · line 2072
$δ T^{μ}_{ν} = - \frac{∣ q ∣ ^{3}}{6 π ^{2} α ^{4} r ^{4}} diag (1, 1, - 3, 1) .$

Scale-invariant irregular extensions

Displayed formulas in this passage

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