Coalgebras and quantization
نویسنده
چکیده
Two coalgebra structures are used in quantum field theory. The first one is the coalgebra part of a Hopf algebra leading to quantization. The second one is a co-module co-algebra over the first Hopf algebra and it is used to define connected chronological products and renormalization. Paper written for the Encyclopaedia of Mathematics. Co-algebra is a pervasive structure of quantum field theory. It enters the quantization of fields, the definition of the chronological product and of renormalization. According to the deformation quantization point of view, quantum fields are classical functions whose product is deformed [1]. This deformation can be described by a co-quasi-triangular structure on the Hopf algebra of normal products [2, 3, 4]. 1 The Hopf algebra of normal products Taking the example of a scalar field, we start from the co-algebra C generated as a vector space by the Wick powers φ(x), where n is a nonnegative integer (x is a point of R). The coproduct of C is given by ∆Cφ (x) = n ∑
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تاریخ انتشار 2008