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In mathematics, and in particular, in the mathematical background of string theory, the Goddard–Thorn theorem (also called the no-ghost theorem) is a theorem about certain vector spaces. It is named after Peter Goddard and Charles Thorn. The name "no-ghost theorem" stems from the fact that in the original statement of the theorem, the vector space inner product is positive definite. Thus, there were no vectors of negative norm for ''r'' ≠ 0. The name "no-ghost theorem" is also a word play on the phrase no-go theorem. == Formalism == Suppose that ''V'' is a vector space with a nondegenerate bilinear form (·,·). Further suppose that ''V'' is acted on by the Virasoro algebra in such a way that the adjoint of the operator ''Li'' is ''L-i'', that the central element of the Virasoro algebra acts as multiplication by 24, that any vector of ''V'' is the sum of eigenvectors of ''L''0 with non-negative integral eigenvalues, and that all eigenspaces of ''L''0 are finite-dimensional. Let ''Vi'' be the subspace of ''V'' on which ''L''0 has eigenvalue ''i''. Assume that ''V'' is acted on by a group ''G'' which preserves all of its structure. Now let of the two-dimensional even unimodular Lorentzian lattice (so that -graded, has a bilinear form (·,·) and is acted on by the Virasoro algebra). Furthermore, let ''P''1 be the subspace of the vertex algebra . (All these spaces inherit an action of ''G'' from the action of ''G'' on ''V'' and the trivial action of ''G'' on if ''r'' ≠ 0, and to if ''r'' = 0. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Goddard–Thorn theorem」の詳細全文を読む スポンサード リンク
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