What is the difference between dynamical symmetry and geometrical symmetry?

In summary, Dynamical symmetry is a hidden symmetry, often related to the dynamics of a system rather than its geometry. An example of this is the Hydrogen atom, which exhibits a full SO(4) symmetry instead of just the expected SO(3) symmetry. This is due to the presence of a conserved vector, the Laplace-Runge-Lenz vector, which is not a result of general geometrical features but rather the specific potential of the Hydrogen atom. Dynamical symmetry breaking is a type of spontaneous symmetry breaking and is an unrelated topic. It can be seen in the isospin of nuclear particles, which is related to the group SU(2).
  • #1
wdlang
307
0
i really can not understand it
 
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  • #2
Hi wdlang! :smile:

What's "dynamical symmetry"?

I googled and wiki'd it, but couldn't find anything. :confused:
 
  • #3
Hi,

are you referring to symmetry breaking ? A symmetry can be dynamically or spontaneously broken.
 
  • #4
humanino said:
Hi,

are you referring to symmetry breaking ? A symmetry can be dynamically or spontaneously broken.

Thanks a lot

dynamically broken?

i seldom hear it. However, spiontaneously symmetry broken is well know.

could you explain it in detail? thanks!
 
  • #5
Here is my humble understanding. A dynamical symmetry is a _hidden_ symmetry. The classic example would be the Hydrogen atom. Naively, we would only expect an SO(3) symmetry associated with rotational symmetry. This would be the geometrical symmetry, which leads to the conserved angular momentum vector. In fact, the full symmetry of the system is SO(4); this is exhibited by there being another conserved vector, the Laplace-Runge-Lenz (LRL) vector.

Since the LRL vector is peculiar to the particular potential of the hydrogen atom and does not emerge as the result of some general geometrical feature shared by a whole class of systems (like rotational symmetry), it is termed a _dynamical_ symmetry. If one were naively observing the Hydrogen atom, then one would only notice the extra symmetry in studying its dynamics.

Disclaimer: This is only what I have gleaned from reading some papers on dynamical symmetry; I have never read an actual definition.

Side notes:
* If I recall correctly, the SO(4) symmetry of the Hydrogen atom can be realized by starting in a four dimensional space and dimensionally reducing. In which case the dynamical symmetry starts out as a geometrical symmetry.

* Dynamical symmetry breaking is a type of spontaneous symmetry breaking and is an unrelated topic.
 
  • #6
I think symmetry is due to dynamic interactions within creation. for example, hydrogen atoms are correct, symmetry in the isospin of nuclear related to the group SU (2)
 

Question 1: What is dynamical symmetry?

Dynamical symmetry refers to the symmetry that is present in the motion or behavior of a system. This means that certain properties or characteristics of the system remain unchanged as it undergoes a transformation or change in time.

Question 2: What is geometrical symmetry?

Geometrical symmetry, also known as static symmetry, refers to the symmetry that is present in the physical shape or structure of an object. This means that the object can be divided into identical parts or sections that are mirror images of each other.

Question 3: How do dynamical and geometrical symmetry differ?

The main difference between dynamical and geometrical symmetry is the aspect of time. Dynamical symmetry deals with the symmetry present in the motion or behavior of a system, while geometrical symmetry deals with the symmetry present in the physical shape or structure of an object.

Question 4: Can a system have both dynamical and geometrical symmetry?

Yes, a system can have both dynamical and geometrical symmetry. For example, a spinning top has both types of symmetry - it maintains its shape (geometrical symmetry) while it rotates (dynamical symmetry).

Question 5: Why is understanding the difference between dynamical and geometrical symmetry important?

Understanding the difference between dynamical and geometrical symmetry is important for scientists because it helps them to better conceptualize and analyze physical systems. It also allows for a more comprehensive understanding of the laws and principles that govern the behavior and structure of these systems.

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