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In theoretical physics, the Batalin–Vilkovisky (BV) formalism (named for Igor Batalin and Grigori Vilkovisky) was developed as a method for determining the ghost structure for Lagrangian gauge theories, such as gravity and supergravity, whose corresponding Hamiltonian formulation has constraints not related to a Lie algebra (i.e., the role of Lie algebra structure constants are played by more general structure functions). The BV formalism, based on an action that contains both fields and "antifields", can be thought of as a vast generalization of the original BRST formalism for pure Yang–Mills theory to an arbitrary Lagrangian gauge theory. Other names for the Batalin–Vilkovisky formalism are field-antifield formalism, Lagrangian BRST formalism, or BV-BRST formalism. It should not be confused with the Batalin–Fradkin–Vilkovisky (BFV) formalism, which is the Hamiltonian counterpart. ==Batalin–Vilkovisky algebras== In mathematics, a Batalin–Vilkovisky algebra is a graded supercommutative algebra (with a unit 1) with a second-order nilpotent operator Δ of degree −1. More precisely, it satisfies the identities *|''ab''| = |''a''| + |''b''| (The product has degree 0) *|Δ(''a'')| = |''a''| − 1 (Δ has degree −1) *(''ab'')''c'' = ''a''(''bc'') (The product is associative) *''ab'' = (−1)|''a''||''b''|''ba'' (The product is (super-)commutative) *Δ2 = 0 (Nilpotency (of order 2)) *Δ(''abc'') − Δ(''ab'')''c'' −(−1)|''a''|''a'' Δ(''bc'') − (−1)(|''a''|+1)|''b''|''b'' Δ(''ac'') + Δ(''a'')''bc'' + (−1)|''a''|''a''Δ(''b'')''c'' + (−1)|''a''| + |''b''|''ab''Δ(''c'') − Δ(1)''abc'' = 0 (The Δ operator is of second order) One often also requires normalization: *Δ(1) = 0 (normalization) 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「Batalin–Vilkovisky formalism」の詳細全文を読む スポンサード リンク
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