What is internal space/internal symmetry?

In summary, exterior symmetry refers to spacetime symmetry and is depicted by the Poincare group. Internal symmetry, such as U(1) and gauge symmetries, do not occur in spacetime but correspond to internal "charges" in the theory. SU(3) and SU(5) are also considered internal symmetries. Internal spin symmetry is not a spacetime symmetry but rotates the spin of particles at a point in spacetime. It can be pictured as acting on tangent spaces at each point, similar to U(1), SU(2), and SU(3) symmetries.
  • #1
yicong2011
75
0
Hi,

I have already been familiar with that exterior symmetry is the spacetime symmetry. Such kind of symmetry has been depicted by Poincare' group.

Then I am still find the concept internal space/internal symmetry ambiguous.

And I cannot understand why put Spin in exterior symmetry not internal symmetry, since there is no space-time variation for Spin.

And I have heard someone told me that exterior symmetry has something to do with U(1) group. I cannot understand it. I think exterior symmetry is associated with Poincare' group.

The last question, are the two concepts internal symmetry and intrinsic symmetry of the same meaning?

Thanks very much.
 
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  • #2
One of my questions has been resolved.

Spin is considered in angular momentum term, so it should have spacetime variation. Thus, it is in exterior symmetry.
 
  • #3
U(1), and gauge symmetries in general, are considered internal symmetries because the transformations are not occurring in spacetime. The symmetries correspond to internal "charges" (the charges are those quantities in the theory that are conserved under the symmetry transformations.) For example, the action of U(1) is to impart a phase shift to the wavefunction (or particle). Saying that two particles that differ by a phase shift are actually the same results in the existence of the electric charge. Mathematically, the theory describing the electromagnetic interaction is invariant under U(1) operations. This is an internal symmetry because there are no spacetime operations (like rotations or translations) that can change the phase of the wavefunction.
 
  • #4
bapowell said:
U(1), and gauge symmetries in general, are considered internal symmetries because the transformations are not occurring in spacetime. The symmetries correspond to internal "charges" (the charges are those quantities in the theory that are conserved under the symmetry transformations.) For example, the action of U(1) is to impart a phase shift to the wavefunction (or particle). Saying that two particles that differ by a phase shift are actually the same results in the existence of the electric charge. Mathematically, the theory describing the electromagnetic interaction is invariant under U(1) operations. This is an internal symmetry because there are no spacetime operations (like rotations or translations) that can change the phase of the wavefunction.


How about SU(3), SU(5)? Are they all internal symmetry?
 
  • #5
yicong2011 said:
How about SU(3), SU(5)? Are they all internal symmetry?
Yup. SU(3) operates on the "color" degrees of freedom which are internal to hadrons. Basically, SU(3) performs a rotation in color-charge space, allowing hadrons to swap colors. Invariance under this operation implies the existence of the strong force, which facilitates the color change.
 
  • #6
I was wondering about this, too. What kind of symmetry is the internal spin symmetry?

It is not a spacetime symmetry, but a symmetry taking place at a point in spacetime. It rotates the spin of point particles. But then also it is in a finite dimensional representation of the Lorentz symmetry.

So can we picture internal spin as acting on little tangent spaces attached at every point in spacetime, just as the U(1), SU(2) and SU(3) internal symmetries?

thanks
 

1. What is internal space?

Internal space, also known as internal degrees of freedom, refers to the dimensions or parameters within a system that are not considered in the external space. These dimensions can include properties such as spin, charge, and color, and are important in understanding the behavior and interactions of particles.

2. What is internal symmetry?

Internal symmetry is a concept in physics that refers to the invariance of a system under transformations within its internal space. This means that the laws of physics governing the system remain unchanged when certain parameters or dimensions of the system are altered. Internal symmetry is an important principle in understanding the fundamental interactions of particles.

3. How is internal space different from external space?

External space, also known as physical space, refers to the three-dimensional space that we experience and interact with in our everyday lives. Internal space, on the other hand, refers to the dimensions or parameters within a system that are not directly observable in physical space. These dimensions can only be understood through mathematical models and theories.

4. What is the role of internal space in particle physics?

Internal space is crucial in particle physics as it allows us to understand the fundamental properties and interactions of particles. By considering the internal degrees of freedom of a system, we can better explain the behavior and properties of particles, such as their spin and mass. Internal space also plays a role in the development of theories, such as the Standard Model, which describe the fundamental particles and their interactions.

5. How is internal space related to quantum mechanics?

In quantum mechanics, particles are described as wave functions that exist in a multidimensional space. This space includes both external and internal dimensions, with internal space being defined by the particle's internal degrees of freedom. The principles of quantum mechanics, such as superposition and entanglement, also apply to internal space, allowing us to understand the behavior of particles on a subatomic level.

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