Dynamics for QCD on an Infinite Lattice
Dynamics for QCD on an Infinite Lattice
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DOI：
10.1007/s00220-016-2733-5
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发表时间：
2015-12
影响因子：
2.4
通讯作者：
H. Grundling;G. Rudolph
中科院分区：
文献类型：
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作者：
H. Grundling;G. Rudolph
我们证明了在无限格点上的Hamilton QCD的动力学自同构群的存在性，这是在C*-代数的背景下完成的。基态的存在也得到了。从Kijowski，Rudolph（cf. J Math Phys 43：1796-1808 [15]，J Math Phys 46：032303 [16]），我们陈述了它的域代数和自然表示。然后，我们将这种表示推广到无限格，并构造一个Hilbert空间，它表示了所有的局部代数（即，与有限连通子格相关联的运动学代数），其配备有正确的分次对易关系。在一个适当大的C*-代数上，我们证明了存在一个单参数自同构群，它是局部时演化沿沿着有限子格序列递增到满格的逐点范数极限.这是我们的全球时间演变。然后，我们把局部代数w.r.t.的所有轨道生成的C*-代数作为我们的域代数。全球时间演变。因此，时间演化创造了场代数。时间演化在这个场代数的选择上是强连续的，尽管在原来的较大的C*-代数上不是。我们定义了规范变换，解释了如何强制高斯定律约束，表明动力学自同构群下降到物理观测量的代数，并证明了规范不变基态的存在。
We prove the existence of the dynamics automorphism group for Hamiltonian QCD on an infinite lattice in, and this is done in a C*-algebraic context. The existence of ground states is also obtained. Starting with the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph (cf. J Math Phys 43:1796–1808 [15], J Math Phys 46:032303 [16]), we state its field algebra and a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e., kinematics algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. On a suitably large C*-algebra acting on this Hilbert space, and containing all the local algebras, we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. We then take as our field algebra the C*-algebra generated by all the orbits of the local algebras w.r.t. the global time evolution. Thus the time evolution creates the field algebra. The time evolution is strongly continuous on this choice of field algebra, though not on the original larger C*-algebra. We define the gauge transformations, explain how to enforce the Gauss law constraint, show that the dynamics automorphism group descends to the algebra of physical observables and prove that gauge invariant ground states exist.