- #1
wdlang
- 306
- 0
i really can not understand it
What is the difference between dynamical symmetry and geometrical symmetry?
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Discussion Overview
The discussion revolves around the concepts of dynamical symmetry and geometrical symmetry, exploring their definitions, differences, and implications within the context of physics. Participants examine examples, particularly focusing on the hydrogen atom, and consider related concepts such as symmetry breaking.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- Some participants express confusion regarding the definition of "dynamical symmetry" and its distinction from "geometrical symmetry."
- One participant suggests that dynamical symmetry may relate to symmetry breaking, noting that symmetries can be dynamically or spontaneously broken.
- A participant provides an explanation of dynamical symmetry as a hidden symmetry, using the hydrogen atom as an example, where the full symmetry is SO(4) rather than just SO(3) associated with rotational symmetry.
- This participant notes that the Laplace-Runge-Lenz vector is an example of a conserved quantity that indicates dynamical symmetry, which is not immediately apparent from geometrical considerations.
- Another participant mentions that symmetry is related to dynamic interactions, referencing isospin symmetry in nuclear physics and the group SU(2).
Areas of Agreement / Disagreement
Participants do not reach a consensus on the definitions and implications of dynamical versus geometrical symmetry, with multiple competing views and interpretations presented throughout the discussion.
Contextual Notes
Some limitations include the lack of formal definitions for dynamical symmetry, the potential dependence on specific examples like the hydrogen atom, and the unresolved nature of how these concepts relate to symmetry breaking.
- #2
tiny-tim
Science Advisor
Homework Helper
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Hi wdlang! 
What's "dynamical symmetry"?
I googled and wiki'd it, but couldn't find anything.
What's "dynamical symmetry"?
I googled and wiki'd it, but couldn't find anything.
- #3
humanino
- 2,523
- 8
Hi,
are you referring to symmetry breaking ? A symmetry can be dynamically or spontaneously broken.
are you referring to symmetry breaking ? A symmetry can be dynamically or spontaneously broken.
- #4
wdlang
- 306
- 0
humanino said:
Thanks a lot
dynamically broken?
i seldom hear it. However, spiontaneously symmetry broken is well know.
could you explain it in detail? thanks！
- #5
cerf
- 1
- 0
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.
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
ha.dnri
- 4
- 0
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)