Manuscript I-B-VP-2@1 · I-B-VP-2-v1.tex · section · f4bd2b11

Definition and compact-test finiteness

The regular host and the spectral covariance › Definition and compact-test finiteness · lines 398–418

I-B-VP-2@1#eq:bisolution

The spectral construction is quasifree and has nonnegative one-particle Hamiltonian $H_{β}$ . It is the specified distinguished spectral state, not a uniqueness theorem among all algebraic ground states.

On regular charts,

P_{X} W_{β} = P_{X^{'}} W_{β} = 0, P = \partial_{t}^{2} - Δ_{q_{N}} = - □_{g} .

These equations follow by spectral calculus and integration by parts on compact tests. Their principal symbol is

p (X, κ) = - κ_{t}^{2} + κ_{r}^{2} + \frac{κ _{φ} ^{2}}{α ^{2} r ^{2}} + κ_{z}^{2},

up to an irrelevant overall sign.

Displayed formulas in this passage

I-B-VP-2@1#eq:bisolution · line 406
$P_{X} W_{β} = P_{X^{'}} W_{β} = 0, P = \partial_{t}^{2} - Δ_{q_{N}} = - □_{g} .$
unlabeled · line 413
$p (X, κ) = - κ_{t}^{2} + κ_{r}^{2} + \frac{κ _{φ} ^{2}}{α ^{2} r ^{2}} + κ_{z}^{2},$

Definition and compact-test finiteness

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