THE PHYSICAL INTERPRETATION OF THE LANCZOS TENSOR

The field equations of general relativity can be written as first-orde r differential equations in the Weyl tensor; the Weyl tensor, in turn, can be written as a first-order differential equation in a three-inde x tensor called the Lanczos tenser. Similarly, in the electromagnetic theory Maxwell's equations can be written as first-order differential equations in the field tensor F-ab and this in turn can be written as a first-order differential equation in the vector potential A(a); thus the Lanczos tensor plays a similar role in general relativity to that of the vector potential in the electromagnetic theory. The Aharonov-B ohm effect shows that when quantum mechanics is applied to electromagn etic theory, the vector potential is dynamically significant, and this leads to an attempt to quantize the gravitational field by pursuing t he analogy between the vector field and the Lanczos tensor.