李场再探
Lie fields revisited
摘要：
利用产生和湮灭算子的变形 *-代数构造了一类相互作用的经典随机场。所构造的场是经典的随机场形式的"李场"。利用真空向量构造了代数上的线性形式，并将其证明为代数上的状态。假设这个猜想是正确的，所构造的场是"量子随机场"，因为它们具有庞加莱不变真空，其涨落尺度由普朗克常数决定。一个非局部粒子解释的形式主义被证明是相同的粒子解释的量子场论。
英文摘要：
A class of interacting classical random fields is constructed using deformed *-algebras of creation and annihilation operators. The fields constructed are classical random field versions of "Lie fields". A vacuum vector is used to construct linear forms over the algebras, which are conjectured to be states over the algebras. Assuming this conjecture is true, the fields constructed are "quantum random fields" in the sense that they have Poincare invariant vacua with a fluctuation scale determined by Planck's constant. A nonlocal particle interpretation of the formalism is shown to be the same as a particle interpretation of a quantum field theory.
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