速度网格上的点形式量子场论I：玻色收缩
Point Form Quantum Field Theory on Velocity Grids I: Bosonic Contractions
摘要：
在连续量子场论的离散时空近似的基础上，研究了连续量子场论的离散速度空间近似。本文给出了一个以具有离散指数的裸费米子-反费米子-玻色子产生和湮灭算符表示的四动量算符。在连续量子场论中，费米子-反费米子的产生和湮灭算符在四动量算符中表现为双线性，并生成一个幺正代数。当模的数目范围仅在有限数目的值上时，代数是与U（2N）的李代数相关联的。通过保持N有限（但任意）的问题，由于一个无限的洛伦兹体积和创建无限数量的裸费米子反费米子对被避免。但是，即使有有限数量的模式，仍然有可能创造出无限数量的裸玻色子。我们展示了如何产生的完整的玻色子代数的压缩限制的另一个单一的代数，限制裸玻色子的数量在任何模式是有限的。有限模哈密顿量的一般性质进行了研究，是几个简单的模型，看到的玻色子收缩的收敛速度;微调裸强耦合常数的可能性，也简要讨论。
英文摘要：
In constrast to discretized space-time approximations to continuum quantum field theories, discretized velocity space approximations to continuum quantum field theories are investigated. A four-momentum operator is given in terms of bare fermion-antifermion-boson creation and annihilation operators with discrete indices. In continuum quantum field theories the fermion-antifermion creation and annihilation operators appear as bilinears in the four-momentum operator and generate a unitary algebra. When the number of modes range over only a finite number of values, the algebra is that associated with the Lie algebra of U(2N). By keeping N finite (but arbitrary) problems due to an infinite Lorentz volume and to the creation of infinite numbers of bare fermion-antifermion pairs are avoided. But even with a finite number of modes, it is still possible to create an infinite number of bare bosons. We show how the full boson algebra arises as the contraction limit of another unitary algebra that restricts the number of bare bosons in any mode to be finite. Generic properties of finite mode Hamiltonians are investigated, as are several simple models to see the rate of convergence of the boson contraction; the possibility of fine tuning the bare strong coupling constant is also briefly discussed.
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