New formulation for the lattice-fermion derivative. Locality and chirality without spectrum doubling.
New formulation for the lattice-fermion derivative. Locality and chirality without spectrum doubling.
复制标题
晶格费米子导数的新公式。
DOI：
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发表时间：
1986
影响因子：
8.6
通讯作者：
Weinstein
中科院分区：
文献类型：
--
作者：
Quinn;Weinstein
我们给出了格点费米子导数的一个公式，它既是局域的，又是显式手性的。只要适当地采用连续介质和无限大体积极限，该公式避免了谱加倍，并且对于Yukawa耦合标量情况给出了一个令人满意的弱耦合微扰理论。对于规范理论，我们发现为了在连续极限中保持正确的弱耦合微扰理论，必须在长弦路径上引入一个和。-提交给物理审查快报*由能源部支持的工作，合同DE AC03 76SF00515。本文提出了一种无~谱倍增的手征费米子局域晶格理论。我们对这个问题的兴趣是因为我们希望发展一种方法，允许对真正的手征规范理论(例如，大多数大统一理论)进行非微扰研究。我们发现，一个人可以避免这种暗示。尼尔森-尼诺米亚定理的“阳离子”，因为与大多数禁止定理一样，它的证明需要一个隐含的假设；即一个人应该先取无限体积的极限，然后再取连续统极限。对于一个最初定义在任何有限体积中的理论，如果仔细考虑无限体积和连续谱极限，避免谱加倍是微不足道的。我们给出了一种显式演示这些性质的方法。我们的公式包含一个附加参数E，它在连续统极限中消失。在较早的一篇文章中，我们讨论了一类没有光谱倍增的局域自由费米子导数。然而，我们发现这些衍生品是领先的。。自由理论中的非协变电流-电流关联函数，以及费米子与标量场通过Yukawa相互作用理论中的非协变传播子。我们的结论是，这些问题只能通过使用SLAC类型的长程导数来避免。这封信的目的是为了证明这一点。在本文中，我们提出了一个局域手征费米子理论，它不仅具有未加倍的光谱，而且在适当取连续谱极限的情况下，还能产生协变的格林函数。不幸的是，当用只引入最短弦路径的通常方法使导数保持规范不变时，所得到的哈密顿量不能正确地重现QED的连续统弱耦合微扰理论。这个问题的根源不在于导数，而在于--
We present a formulation for the lattice fermion derivative which is both -local and explicitly chiral. Provided that the continuum and infinite volume limits are taken properly the formulation avoids spectrum doubling, and gives a satisfactory weak coupling perturbation theory for the case of Yukawa-coupled scalars. For gauge theories we find that a sum over long string paths must be introduced in order to maintain the correct weak-coupling perturbation theory in the continuum limit. -Submitted to Physical Review Letters * Work supported by the Department of Energy, contract DE AC03 76SF00515. .In this paper we present a local lattice theory of chiral fermions which is -_ free of~spectrum doubling. Our interest in this problem is motivated by a desire to develop methods which allow a non-perturbative study of truly chiral gauge theories (e.g., most grand-unified theories). We find that one can avoid the impli. cations of the Nielsen-Ninomiya theorem’ because, as with most no-go theorems, its proof requires an implicit assumption; namely that one should take the limit of infinite volume before taking the continuum limit. For a theory initially de_ fined in any finite volume, it is trivial to avoid spectrum doubling if one takes the in-finite volume and continuum limits carefully. We present a method which explicitly demonstrates these properties. Our formulation involves an additional parameter E which vanishes in the continuum limit. In an earlier paper’ we addressed a class of local free fermion derivatives which have no spectrum doubling. However, we found that these derivatives lead . . to non-covariant current-current correlation functions in the free theory and to non-covariant propagators in the case of the theory of a fermion interacting with a scalar field through a Yukawa interaction. We concluded that these problems could only be avoided by using a long-range derivative of the SLAC type. The purpose of this letter is to demonstrate that this In this paper we present a local chiral fermion theory which not only has an undoubled spectrum but which also produces covariant Green’s functions provided that the continuum limit is properly taken. Unfortunately, when this derivative is rendered gauge invariant by the usual technique of introducing only the shortest string-paths, the resulting Hamilto-nian does not correctly reproduce continuum weak-coupling perturbation theory for QED. The origin of this problem lies not in the derivative but in-the way the