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arXiv 0908.2439quant-phhep-th
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量子化电磁场的经验等效随机场

An empirically equivalent random field for the quantized electromagnetic field

Peter Morgan

摘要:

构造了一个与量子化电磁场经验等价的随机场。随机场和量子化电磁场的产生和湮灭算子代数之间的映射提供了代数和由这些代数上的真空态生成的希尔伯特空间之间的函子。函子不可避免地不会扩展到由随机场和量子化电磁场生成的局部代数之间的函子关系,但是真空态提供的经验内容通过希尔伯特空间恢复了经验等价。从一个创造和湮灭代数到另一个的同构不是平移不变的,因为它依赖于将一个螺旋度的正频率模式映射到等效的负频率模式,但是这两个独立的理论以同样明确的定义和明显的洛伦兹和平移协变的方式呈现。

英文摘要:

A random field that is empirically equivalent to the quantized electromagnetic field is constructed. A mapping between the creation and annihilation operator algebras of a random field and of the quantized electromagnetic field provides a functor between the algebras and the Hilbert spaces generated by the vacuum states over those algebras. The functor inevitably does not extend to a functorial relationship between the local algebras generated by the random field and by the quantized electromagnetic field, but the empirical content provided by the vacuum state restores an empirical equivalence through the Hilbert spaces. The isomorphism from one creation and annihilation algebra to the other is not translation invariant because it depends on mapping positive frequency modes of one helicity to equivalent negative frequency modes, but the two theories taken independently are presented in equally well-defined and manifestly Lorentz and translation covariant ways.

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