What is the relationship between scalar fields and tensor fields?

In summary, The conversation discusses the concept of tensors and their relation to scalar and vector fields. It is mentioned that scalar fields are considered tensors of rank or order zero, while vector fields are considered tensors of rank or order one. The Higgs is mentioned as an example of a scalar field, which would make it a tensor field of rank 0. However, it is noted that in common language, the Higgs is referred to as a scalar field and not a tensor field. The conversation suggests reading more about tensors for further understanding and clarifies that the usual parlance refers to a rank-2 tensor when just using the term "tensor".
  • #1
tionis
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I've PMd some of you with this question, but I got some conflicting replies or no replies at all lol, so I'm posting it here. I also did a Google search and found this which I'm almost sure answers my question, but I just want to confirm with you guys:

''In general, scalar fields are referred to as tensor fields of rank or order zero whereas vector fields are called tensor fields of rank or order one.''

Since the Higgs is a scalar field, I guess it's a tensor field of rank 0, too. Is that correct?
 
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  • #2
Maybe in some technical sense, but nobody calls it that.

And please ask questions on the forum and not by PMing random people.
 
  • #3
Vanadium 50 said:
Maybe in some technical sense, but nobody calls it that.

Vanadium 50, could you please elaborate? This is exactly the kind of replies I was getting via PMs lol.
 
  • #4
Your question is about language, not about physics/mathematics.
The mathematical concept of tensors has a parameter "nth order", which is used for tensors of 2., 3., ... order. You can consider "tensors of 1st order" and "tensors of 0th order", but everyone calls them vectors and scalars, respectively.
 
  • #5
tionis said:
''In general, scalar fields are referred to as tensor fields of rank or order zero whereas vector fields are called tensor fields of rank or order one.''

Since the Higgs is a scalar field, I guess it's a tensor field of rank 0, too. Is that correct?

Yes. But people will look at you funny if you call it that. If you want more detail you might read about tensors on Wikipedia: http://en.wikipedia.org/wiki/Tensor

In the usual parlance, the field of a spin-0 particle like the Higgs is called a scalar field, the field of a spin-1 particle is called a vector field, and the field of a spin-2 particle is called a tensor field. Just saying "tensor" without specifying the rank is understood to mean a rank-2 tensor.
 

1. What is a tensor field?

A tensor field is a mathematical concept used in physics to describe the properties of a physical system, such as the distribution of mass or energy. It is a function that assigns a tensor to every point in a space.

2. What is the Higgs field?

The Higgs field is a theoretical field that permeates all of space and is responsible for giving particles their mass. It is a fundamental part of the Standard Model of particle physics.

3. How is the Higgs field related to the Higgs boson?

The Higgs field is the theoretical concept, while the Higgs boson is the particle associated with the field. The Higgs boson is the particle that was detected by the Large Hadron Collider in 2012, providing evidence for the existence of the Higgs field.

4. Is the Higgs field a scalar or a tensor field?

The Higgs field is a scalar field, meaning that it has a single value at each point in space. This value determines the strength of the Higgs field at that point, which in turn determines the mass of particles that interact with it.

5. Why is it important to determine if the Higgs is a tensor field?

Determining the nature of the Higgs field, whether it is a scalar or tensor, has implications for our understanding of the fundamental forces and particles in the universe. It also helps to further validate the Standard Model of particle physics and could potentially lead to new discoveries and advancements in our understanding of the universe.

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