Non-commutative flux representation for loop quantum gravity
Non-commutative flux representation for loop quantum gravity
复制标题
圈量子引力的非交换通量表示
DOI：
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Johannes Tambornino
中科院分区：
文献类型：
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作者：
A. Baratin;Bianca Dittrich;D. Oriti;Johannes Tambornino
回路量子引力的希尔伯特空间通常用规范联系的柱面泛函来描述，电通量充当非对易导数。长期以来，人们一直认为，这种非对易性阻止了环路量子引力的二重流(或三联体)表示的存在。相反，我们在这里表明，这样的表示可以通过定义在回路引力状态空间上的非对易傅立叶变换来显式定义。在这种对偶表示中，通量算符通过⋆乘法作用，完整算符通过平移作用。我们描述了规范不变对偶态，并讨论了它们的几何意义。最后，我们将这种构造应用于U(1)规范群的更简单的情况，并将所得到的通量表示与回路量子宇宙学中使用的三元表示进行了比较。
The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by ⋆-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.
影响因子：
3.5
作者：
J. Barrett;R. J. Dowdall;W. Fairbairn;F. Hellmann;R. Pereira
通讯作者：
J. Barrett;R. J. Dowdall;W. Fairbairn;F. Hellmann;R. Pereira