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首页> 外文期刊>Annales Henri Poincare >Generating Functions for Lattice Gauge Models with Scaled Fermions and Bosons
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Generating Functions for Lattice Gauge Models with Scaled Fermions and Bosons

机译：用缩放费米子和玻色子的晶格计模型产生函数

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摘要

Recently, employing an imaginary-time functional integral formulation, we considered abelian and nonabelian (aZ)d lattice quantum field gauge theories with new a-dependent locally scaled Wilson Fermi and Bose fields in d4 spacetime dimensions and neglecting the pure gauge interaction. The use of scaled fermions and bosons preserves Osterwalder-Schrader positivity and the spectral content of the models since the decay rates of correlations in the infinite-time limit are unchanged. In addition, scaled fields also result in a less singular, more regular behavior in the continuum limit. The scaled field gauge models are thermodynamically stable, which shows that stability does not depend on the presence of a pure gauge, plaquette term in the action. The finite lattice free energy is bounded with a bound independent of the number of points of the lattice and the lattice spacing a(0,1]. Recall that the expansion of the fermionic exponential bond factor, arising from the interacting nearest neighbor hopping terms in the action, is finite by Pauli exclusion. The Bose-Gauge models we consider here have a finite truncation of the bond factor; the Fermi-mimicking truncated Bose models still obey Osterwalder-Schrader positivity. We show boundedness of the n-point scaled field generating functions and n-point scaled field correlations. The bounds are independent of the number of lattice points and the lattice spacing a(0,1]. For the truncated Bose models, the bound is also independent of the location of the n points. No renormalization of the parameters is needed. The precise a-dependent factors have been extracted and isolated from the unscaled field partition functions and correlations so that the scaled field free energies and correlations are not singular for a(0,1].
机译：最近，采用虚线功能整体的配方，我们考虑了Abelian和Nonabelian（AZ）D格量子磁场测量仪表，具有新的A依赖于局部划分的威尔逊费米和D4时空尺寸的Bose领域，并忽略了纯粹的仪表相互作用。由于无限时间限制中的相关性的衰减率不变，因此使用缩放的费粒和玻色子保留了Osterwalder-Schrader积极性和模型的光谱含量。此外，缩放字段还会导致连续体限制中的较少的奇异，更规则的行为。缩放的现场规格模型是热力学稳定的，表明稳定性不依赖于作用中纯规的斑块术语。有限晶格自由能量与与晶格的点数无关的束缚，晶格间距A（0,1]。回想一下，从互动最近邻居跳跃术语产生的Fermionic指数债券因子的扩展行动是Pauli排除的有限。我们认为这里的Bose-Gauge模型有一个有限的债券因子截断; Fermi-Mimicing截断的BOSE模型仍然服从Osterwalder-Schrader积极性。我们显示了N点缩放字段的界限生成功能和n点缩放的场相关关系。边界独立于格子点的数量和晶格间距A（0,1]。对于截断的BOSE模型，绑定也与N点的位置无关。不需要参数的重整化。从未扫描的现场分区功能和相关性提取和隔离了精确的A相关因素，使得缩放的现场无限能量和相关性ONS不是单数的（0,1]。

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