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« Pur romantique » avant que ne triomphe en France ce courant littéraire, Adam Mickiewicz est, avec Norwid (1821-1883) et Slowacki (1809-1849), le plus grand des poètes polonais du XIXe siècle.

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Chaque fiche de lecture présente une œuvre clé de los angeles littérature ou de los angeles pensée. Cette présentation est couplée avec un article de synthèse sur l’auteur de l’œuvre.

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The formula is called the infinitesimal homotopy relation. It reads LX ω = (d iX + iX d)ω. 4. PHYSICAL APPLICATIONS 41 rule. From the derivation property of the Lie derivative, we immediately deduce that that the formula works for any p-form. That the formula is true for functions should be obvious: Since iX f = 0 by definition, we have (d iX + iX d)f = iX df = df (X) = Xf = LX f. 57) To show that the formula works for one forms, we evaluate (d iX + iX d)(fν dxν ) = d(fν X ν ) + iX (∂µ fν dxµ dxν ) = ∂µ (fν X ν )dxµ + ∂µ fν (X µ dxν − X ν dxµ ) = (X ν ∂ν fµ + fν ∂µ X ν )dxµ .

In particular the phase space for a spin is not the cotangent bundle of the configuration space. This has to be so: we learned from Nils Bohr that a 2n-dimensional phase space contains roughly one quantum state for every h ¯ n of phase-space volume. A cotangent bundle always has infinite volume so its corresponding Hilbert space is necessarily infinite dimensional. A quantum spin, however, has a finite-dimensional Hilbert space so its classical phase space must have a finite total volume. This finite-volume phase space seems unnatural in the traditional view of mechanics, but it fits comfortably into modern the symplectic picture.

52) p−1 slots Acting on a 0-form, iX is defined to be 0. This procedure is called the interior multiplication by X. 53) but it is convenient to have a special symbol for this operation. 54) even though iX involves no differentiation. For example, if X = X µ ∂µ , then iX (dxµ ∧ dxν ) = dxµ ∧ dxν (X α ∂α , ), = X µ dxν − dxµ X ν , = (iX dxµ ) ∧ (dxν ) − dxµ ∧ (iX dxν ). 55) One reason for introducing iX is that there is a nice (and profound) formula for the Lie derivative of a p-form in terms of iX .

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