- #1
Nikratio
- 13
- 0
Hi,
How does one define symmetry of a system?
I believe that a scalar function [tex]g(\vec x)[/tex] is called symmetric under a transformation [tex]\vec F(\vec x) [/tex] if and only if [tex]g(\vec x) = g(\vec F(\vec x))[/tex]
If there is an equivalent criteria for vector functions, I would be inclined to define a system as symmetric under a transformation if all its observables are symmetric under this transformation. Is that correct?
However, how does a vector function need to behave in order to be called symmetric? If the transformation is just a translation in space, we we want all the cartesian components to be invariant, just like individual scalar functions. On the other hand, if the transformation is a rotation, we want the cartesian components to rotate accordingly. But what is the general pattern here? How do the components of a vector valued function have to transform under a general transformation, in order for the function to be called symmetric under this transformation?
How does one define symmetry of a system?
I believe that a scalar function [tex]g(\vec x)[/tex] is called symmetric under a transformation [tex]\vec F(\vec x) [/tex] if and only if [tex]g(\vec x) = g(\vec F(\vec x))[/tex]
If there is an equivalent criteria for vector functions, I would be inclined to define a system as symmetric under a transformation if all its observables are symmetric under this transformation. Is that correct?
However, how does a vector function need to behave in order to be called symmetric? If the transformation is just a translation in space, we we want all the cartesian components to be invariant, just like individual scalar functions. On the other hand, if the transformation is a rotation, we want the cartesian components to rotate accordingly. But what is the general pattern here? How do the components of a vector valued function have to transform under a general transformation, in order for the function to be called symmetric under this transformation?