Invariant Tensors and Lorentz Transformation

In summary, the conversation discusses the topic of invariant tensors under Lorentz transformation and whether there are any other such tensors besides the Kronecker delta and Levi-Civita epsilon. The question is raised on how to find all invariant tensors under a linear transformation and whether there is a general procedure for this. It is also mentioned that tensors, by definition, are invariant objects.
  • #1
Heirot
151
0
It is often stated that the Kronecker delta and the Levi-Civita epsilon are the only (irreducible) invariant tensors under the Lorentz transformation. While it is fairly easy to prove that the two tensors are indeed invariant wrt Lorentz transformation, I have not seen a proof that there aren't any more such tensors.

So, my question is, how to find all invariant tensors under some (linear) transformation? Is there a general procedure for this?

Thanks
 
Physics news on Phys.org
  • #2
If an object is a full tensor, then it should be invariant under any linear transformation, shouldn't it?
 
  • #3
Tensors as per definition are invariant objects, I guess the OP asked about tensor components in the canonical basis.
 

Related to Invariant Tensors and Lorentz Transformation

1. What are invariant tensors?

Invariant tensors are mathematical objects that remain unchanged under a specific transformation. They are used in various fields of science, such as physics and engineering, to describe physical quantities that do not change regardless of the coordinate system or frame of reference.

2. How are invariant tensors used in physics?

Invariant tensors play a crucial role in physics, especially in the theory of relativity. They are used to describe physical quantities, such as energy, momentum, and mass, that have the same value in all inertial reference frames. They also help to simplify equations and make them more elegant and concise.

3. Can you give an example of an invariant tensor?

One example of an invariant tensor is the metric tensor in general relativity. It describes the geometry of spacetime and remains invariant under coordinate transformations. This tensor is crucial in Einstein's theory of relativity and helps to determine the curvature of spacetime.

4. How do invariant tensors differ from other tensors?

Unlike other tensors that change under coordinate transformations, invariant tensors remain unchanged. This property makes them particularly useful in physics, where physical laws should hold true regardless of the reference frame. Invariant tensors are also independent of the choice of coordinates, making them more fundamental and universal.

5. How are invariant tensors calculated?

The calculation of invariant tensors depends on the specific transformation and the properties of the tensor. In general, they can be calculated using matrix operations, such as multiplication and inversion, or tensor calculus. Invariant tensors can also be derived from other tensors by applying certain mathematical operations, such as contraction and symmetrization.

Similar threads

I How to derive irreducible representations/tensors?
    • Special and General Relativity
Replies
22
Views
2K
I Are there non-smooth metrics for spacetime (without singularities)?
    • Cosmology
Replies
3
Views
1K
I What is the relationship between the Hamiltonian and Lorentz invariance?
    • Classical Physics
Replies
6
Views
3K
B Deriving Lorentz Transformation: Wave Eq Invariance & General Relativity
    • Special and General Relativity
Replies
1
Views
1K
I Lorentz Invariance of Q in Weinberg: Justifying Transformation
    • Special and General Relativity
Replies
9
Views
1K
Lorentz invariance of the Minkowski metric
    • Special and General Relativity
Replies
24
Views
7K
A Is the Metric Tensor Invariant under Lorenz Transformations in M4?
    • Special and General Relativity
Replies
5
Views
3K
A [Diff Forms & Skyrmions] What is this called?
    • Differential Geometry
Replies
3
Views
1K
Invariance: What Does it Mean?
    • Special and General Relativity
Replies
5
Views
1K
A How does Lorentz invariance help evaluate tensor integrals?
    • Quantum Physics
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top