Manuscript I-B-VP-0@1 · I-B-VP-0-v1.tex · section · 8a9d0682

Compatibility with the even observables

Properties and information carried by the current › Compatibility with the even observables · lines 883–912

I-B-VP-0@1#eq:wick, I-B-VP-0@1#eq:stress

For reference, set

P_{β} = α^{- 2} (1 - 6 β (1 - β)) - 1, C_{β} = α^{- 4} (1 - 30 β^{2} (1 - β)^{2}) - 1.

With the same complex-field normalization, I-B-VP-v2 proves CheungIBVP (:phi2, :T-complex)

F_{β} := ⟨ Φ^{†} Φ ⟩_{ren} ⟨ T^{μ}_{ν} ⟩_{ren} = \frac{P _{β}}{48 π ^{2} r ^{2}}, = \frac{C _{β}}{720 π ^{2} r ^{4}} diag (1, 1, - 3, 1) + 2 (ξ - \frac{1}{6}) \frac{P _{β}}{48 π ^{2} r ^{4}} diag (4, - 2, 6, 4) .

Their mixed-component order is $(t, r, φ, z)$ . Both are even under $β \leftrightarrow 1 - β$ . The current is odd. Its $ξ$ -independence is consistent with (eq:wick)–(eq:stress): on the regular host, changing $ξ$ changes the stress-tensor improvement but neither the chosen equation, the spectral state, nor the internal Noether current.

Displayed formulas in this passage

I-B-VP-0@1#eq:wick · line 893
$F_{β} := ⟨ Φ^{†} Φ ⟩_{ren} ⟨ T^{μ}_{ν} ⟩_{ren} = \frac{P _{β}}{48 π ^{2} r ^{2}}, = \frac{C _{β}}{720 π ^{2} r ^{4}} diag (1, 1, - 3, 1) + 2 (ξ - \frac{1}{6}) \frac{P _{β}}{48 π ^{2} r ^{4}} diag (4, - 2, 6, 4) .$
I-B-VP-0@1#eq:stress · line 893
$F_{β} := ⟨ Φ^{†} Φ ⟩_{ren} ⟨ T^{μ}_{ν} ⟩_{ren} = \frac{P _{β}}{48 π ^{2} r ^{2}}, = \frac{C _{β}}{720 π ^{2} r ^{4}} diag (1, 1, - 3, 1) + 2 (ξ - \frac{1}{6}) \frac{P _{β}}{48 π ^{2} r ^{4}} diag (4, - 2, 6, 4) .$
unlabeled · line 886
$P_{β} = α^{- 2} (1 - 6 β (1 - β)) - 1, C_{β} = α^{- 4} (1 - 30 β^{2} (1 - β)^{2}) - 1.$

Compatibility with the even observables

Displayed formulas in this passage

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