Quantum‐mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II
Quantum‐mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II
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所有多项式哈密顿量的量子力学路径积分与维纳测度。
DOI：
10.1063/1.526803
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发表时间：
1985
影响因子：
1.3
通讯作者：
J. Klauder
中科院分区：
文献类型：
--
作者：
I. Daubechies;J. Klauder
在扩散常数发散的极限下，给出并证明了量子传播子的相干态表示为连续相空间路径上包含Wiener测度的定义明确的相空间路径积分.这种构造涵盖了广泛的一类自伴哈密顿算子，包括海森堡算子中的所有多项式;事实上，这种方法也适用于不具有自伴扩张的极大对称哈密顿算子。这种构造也导致了正则变换下路径积分的自然协方差。对自旋变量的完全平行的讨论导致了任意自旋算符哈密顿量的传播子的表示为包含单位球上维纳测度的明确定义的路径积分，同样是在扩散常数发散的极限下。
The coherent‐state representation of quantum‐mechanical propagators as well‐defined phase‐space path integrals involving Wiener measure on continuous phase‐space paths in the limit that the diffusion constant diverges is formulated and proved. This construction covers a wide class of self‐adjoint Hamiltonians, including all those which are polynomials in the Heisenberg operators; in fact, this method also applies to maximal symmetric Hamiltonians that do not possess a self‐adjoint extension. This construction also leads to a natural covariance of the path integral under canonical transformations. An entirely parallel discussion for spin variables leads to the representation of the propagator for an arbitrary spin‐operator Hamiltonian as well‐defined path integrals involving Wiener measure on the unit sphere, again in the limit that the diffusion constant diverges.