倒易相对论下世界线不变量系统的约束量子化。II
Constraint quantisation of a worldline system invariant under reciprocal relativity. II
摘要：
我们考虑在互易相对论对称性下系统的世界线量子化不变。在物理状态上施加第一类约束，即局部时间重新参数化的生成器，强制将世界线宇宙学常数与四辛对称群Q（3，1）~ U（3，1）x H（4）的二次Casimir的固定值等同起来，Q（3，1）~ U（3，1）x H（4）是伪酉群与Weyl-Heisenberg群的半直积。在我们之前的论文J Phys A 40（2007）12095- 12111中，“自旋”自由度被处理为协变振荡器，导致宇宙学常数的独特选择，这是从物理规范不变态投影出负范数态所需的。在本文中，自旋自由度被视为具有正范数态的标准振子（其中洛伦兹提升在辅助空间中不是数量守恒的;倒易变换当然一般不是自旋守恒的）。在协变方法中，能量-动量矢量的平方的谱在整个实数线上是连续的，因此包括快子（类空）和零分支。采用标准框架，在每个分支上实现Wigner方法，将辅助空间分解为相应小代数和附加退化代数的酉不可约表示.与协变方法相比，物理状态空间大大丰富，包含整数自旋质量态的塔，以及非常规的无质量表示，具有连续的欧几里得动量和任意整数螺旋度。
英文摘要：
We consider the world-line quantisation of a system invariant under the symmetries of reciprocal relativity. Imposition of the first class constraint, the generator of local time reparametrisations, on physical states enforces identification of the world-line cosmological constant with a fixed value of the quadratic Casimir of the quaplectic symmetry group Q(3,1) ~ U(3,1) x H(4), the semi-direct product of the pseudo-unitary group with the Weyl-Heisenberg group. In our previous paper, J Phys A 40 (2007) 12095--12111, the `spin' degrees of freedom were handled as covariant oscillators, leading to a unique choice of cosmological constant, required for projecting out negative-norm states from the physical gauge-invariant states. In the present paper the spin degrees of freedom are treated as standard oscillators with positive norm states (wherein Lorentz boosts are not number-conserving in the auxiliary space; reciprocal transformations are of course not spin-conserving in general). As in the covariant approach, the spectrum of the square of the energy-momentum vector is continuous over the entire real line, and thus includes tachyonic (spacelike) and null branches. Adopting standard frames, the Wigner method on each branch is implemented, to decompose the auxiliary space into unitary irreducible representations of the respective little algebras and additional degeneracy algebras. The physical state space is vastly enriched as compared with the covariant approach, and contains towers of integer spin massive states, as well as unconventional massless representations, with continuous Euclidean momentum and arbitrary integer helicity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
