Why Do Textbooks Use Different Signs in Gauge Covariant Derivative Notations?

[captain]

I was wonder why some textbooks define it as D_u=d_u-ieA_u and other textbooks define it as D_u=d_u+ieA_u. I am not clear whether this choice doesn't matter or is one notation correct.

 

[dextercioby]

It's not relevant, it"s simply a matter of convention and convenience. It has to do with the connection between "e" and the value of the electric charge of the electron.

 

[denian]

The choice of notation for the gauge covariant derivative can vary between textbooks and can often be confusing. However, both notations are correct and ultimately represent the same mathematical concept.

The difference in notation arises from the convention used to define the sign of the electric charge in the gauge theory. In some textbooks, the electric charge is defined as a positive quantity, while in others it is defined as a negative quantity. This difference in definition leads to the difference in sign between the two notations for the gauge covariant derivative.

In terms of physical significance, the choice of notation does not matter as long as it is consistent within a particular textbook or mathematical framework. The important thing is to understand the underlying concept of the gauge covariant derivative, which is to take into account the effects of a gauge field (represented by A_u in the equations) when differentiating a field (represented by d_u in the equations) in a gauge theory.

In summary, both notations for the gauge covariant derivative are correct and the choice between them is a matter of convention. it is important to understand the concept behind the equation rather than getting caught up in the notation used.