Weak values and the Aharonov-Vaidman gauge

作者：Parks A D^*

来源：Journal of Physics A-Mathematical and Theoretical, 2010, 43(3): 035305.

DOI：10.1088/1751-8113/43/3/035305

The Aharonov-Vaidman gauge-which additively transforms the mean value of a quantum mechanical observable into an associated weak value-is introduced. It is shown that the unusual eccentric properties of weak values are inherited from this gauge and that a weak value of an observable can be considered as its mean value measured in the Aharonov-Vaidman gauge. The total time derivative of this sum also transforms an observable's mean value equation of motion into the associated weak value equation of motion and it is shown that the weak energy of evolution which influences the evolution of a weak value is intrinsic to the rate of change of the Aharonov-Vaidman gauge. Both of these equations of motion can be expressed in terms of time varying generalized coordinates and their rates of change. These equations satisfy the Euler-Lagrange equations which-in turn-define conjugate momenta and provide for their coordinate/momentum/time Poincare representations. The underlying mathematical forms of these two representations are identical except for three symbols which distinguish them physically and identify three simple replacement operations that are required to transform the mean value Poincare representation into the weak value Poincare representation. This transformational relationship between Poincare representations defines the notion of quasi-form invariance and the replacement operations encode the peculiar physical properties induced by the Aharonov-Vaidman gauge, i.e. the complexification and increased dimension of phase space, and the absorption of the weak energy of evolution by the conjugate momenta. Simple examples are used to illustrate the theory.

• 出版日期2010-1-22