What is the relationship between scalar fields and tensor fields?

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Discussion Overview

The discussion centers on the relationship between scalar fields and tensor fields, particularly in the context of their definitions and classifications within physics and mathematics. Participants explore the terminology used to describe these concepts and the implications of calling scalar fields tensor fields of rank zero.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant states that scalar fields are tensor fields of rank or order zero, while vector fields are tensor fields of rank or order one, seeking confirmation of this classification.
  • Another participant suggests that while the classification may be technically correct, it is not commonly used in practice.
  • A participant emphasizes that the discussion is more about language than the underlying physics or mathematics.
  • It is noted that the mathematical concept of tensors includes an "nth order" parameter, and while scalars and vectors can be considered tensors of order zero and one respectively, the conventional terminology tends to favor the terms "scalar" and "vector."
  • One participant agrees with the classification of the Higgs field as a tensor field of rank zero but warns that using this terminology may lead to confusion.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of referring to scalar fields as tensor fields of rank zero. There is no consensus on the terminology, as some participants acknowledge the technical correctness while others highlight the lack of common usage.

Contextual Notes

The discussion reveals a potential limitation in the understanding of tensor classifications and the informal conventions used in the field, which may lead to misunderstandings when discussing these concepts.

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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Maybe in some technical sense, but nobody calls it that.

And please ask questions on the forum and not by PMing random people.
 
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.
 
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.
 
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.
 

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