论文标题
海森伯格与协变量弦
Heisenberg versus the Covariant String
论文作者
论文摘要
大量特征的庞加尔多重$ \ bigl（p^2-m^2 \ bigr）ψ= 0 $不能是具有$ d $ -d $ - 向量位置运算符$ x =（x_0，x_0，\ dots x__ {d-1}）的子空间的子空间简单的论点是，每个庞加莱的多重质量都消失了。 诺伊曼定理的结论得出相同的结论。 在量子理论中，即使Dirac对相应的经典约束的处理可以定义具有一致的相应量子模型的象征性亚序列，但绝对连续频谱对较低的尺寸亚曼型的约束也会产生零。它的希尔伯特空间不是无约束理论的子空间。因此，无约束模型的操作员关系不必延续到受约束的模型中。 我们的论点不包括量化的相对论粒子的世界线模型和协变量量子字符串的物理状态。 我们纠正了对作用于粒子的洛伦兹变换的发生器的误解。
A Poincaré multiplet of mass eigenstates $\bigl(P^2 - m^2\bigr)Ψ= 0$ cannot be a subspace of a space with a $D$-vector position operator $X=(X_0,\dots X_{D-1})$: the Heisenberg algebra $[P^m, X_n] = i δ^m{}_n$ implies by a simple argument that each Poincaré multiplet of definite mass vanishes. The same conclusion follows from the Stone-von Neumann theorem. In a quantum theory the constraint of an absolutely continuous spectrum to a lower dimensional submanifold yields zero even if Dirac's treatment of the corresponding classical constraint defines a symplectic submanifold with a consistent corresponding quantum model. Its Hilbert space is not a subspace of the unconstrained theory. Hence the operator relations of the unconstrained model need not carry over to the constrained model. Our argument excludes quantized worldline models of relativistic particles and the physical states of the covariant quantum string. We correct misconceptions about the generators of Lorentz transformations acting on particles.
