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2
votes
3answers
531 views

What is a nonlinear field?

I have read two possible definitions. A nonlinear field is A field taking values on a manifold. A field whose equation is nonlinear. What do you understand by a nonlinear field or a nonlinear ...
6
votes
1answer
1k views

What is a chiral field?

I have not found a clear definition of this. A teacher told me that it was a field having some constrains but that is not very convincing for me. He told me also that some examples could be skyrme ...
17
votes
3answers
2k views
7
votes
1answer
568 views

Is Bose-Einstein condensate a good example of a classical massive boson field?

Physically, we know that a BEC has formed if a macroscopic number of bosons occupy a single quantum state. The wave-function $\Psi(x)$ of the latter, normalized to the total number of condensed atoms ...
9
votes
4answers
491 views

Why must the field equations be differential?

In Landau–Lifshitz's Course of Theoretical Physics, Vol. 2 (‘Classical Fields Theory’), Ch. IV, § 27, there is an explanation why the field equations should be linear differential equations. It goes ...
59
votes
10answers
8k views

What is a field, really?

There was a reason why I constantly failed physics at school and university, and that reason was, apart from the fact I was immensely lazy, that I mentally refused to "believe" more advanced stuff ...
8
votes
2answers
334 views

Does Noether's theorem also give rise to quantities conserved over space?

Noether's theorem gives rise to quantities that are conserved over time. But does it also give rise to quantities that are conserved over space?
7
votes
1answer
430 views

What corresponds to this Lagrangian density?

Is there a physical example of a field that would have the following Lagrangian density $$ L= \sqrt{1+\phi_x^2 +\phi_y^2+\phi_z^2} $$ where the subscripts denote partial derivatives and $\phi$ is a ...
8
votes
2answers
396 views

Quantizing EM field

Why when we quantize EM field, whe quantize the vector potential $A^\mu$ obtaining vectorial particles (photons) like the elastic field (phonons) and we can't quantize directly the EM-field tensor ...
6
votes
3answers
568 views

What are fields?

I'm following my first course in field theory and the professor began, like many books do, by introducing the scalar field. However, I am a bit hesitant about the physical idea of fields. My question ...
5
votes
1answer
326 views

formal framework for talking about 'minimal couplings'

usually on physical theories one would have Lagrangians or Hamiltonians with multiple fields; say, a vector $A_{\mu}$ and a scalar $\phi$ and one would postulate ad hoc a coupling between the fields ...
15
votes
4answers
2k views

History of Electromagnetic Field Tensor

I'm curious to learn how people discovered that electric and magnetic fields could be nicely put into one simple tensor. It's clear that the tensor provides many beautiful simplifications to the ...
5
votes
1answer
630 views

Einstein's Field equations and impulse-energy tensor

I premise that I haven't yet studied General Relativity, but in Relativistic Electrodymaics I have knowed impulse-energy tensor of Electromagnetic Field. I know in Einstein's equations there is ...
9
votes
1answer
4k views

The Euler-Lagrange equation in special relativity

How can I derive the Euler-Lagrange equations valid in the field of special relativity? Specifically, consider a scalar field.
6
votes
2answers
2k views

What does a Field Theory mean?

What exactly is a field theory? How do we classify theories as field theories and non field theories? EDIT: After reading the answers I am under the impression that almost every theory is a ...