Thanks!Demystifier said:No, in general they are just covariant. For electrodynamics the equations of motion are invariant under gauge transformations, but for Yang-Mills theories they are just covariant. Similarly, the Einstein-Hilbert action is invariant under general coordinate transformations, but the Einstein equation of motion is just covariant.
Gauge transformations are mathematical transformations that are used to describe symmetries in physical systems. They involve changing the mathematical description of a system without affecting its physical properties.
Equations of motion are mathematical equations that describe the motion of a physical system. They are typically used in classical mechanics to determine the position, velocity, and acceleration of an object at a given time.
Gauge transformations are related to equations of motion because they can be used to transform the equations of motion into a different form without changing their physical meaning. This allows for different mathematical descriptions of the same physical system.
Yes, equations of motion are invariant under gauge transformations. This means that the physical properties described by the equations of motion remain the same even after a gauge transformation is applied.
Gauge transformations are important in physics because they allow for a more flexible and comprehensive understanding of physical systems. They also help to reveal underlying symmetries and principles that govern the behavior of these systems.