Tagged Questions
1
vote
1answer
104 views
Potential in Relativistic Scalar Field Theory
My intention is to establish a Soliton equation. I have cropped a page from Mark Srednicki page no 576.
I have understand the equation (92.1) but don't understand that how they guessed the ...
0
votes
1answer
75 views
Higher order covariant Lagrangian
I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
-1
votes
1answer
75 views
Linear/ non linear Scalar field theory
How do I understand that the action for the free relativistic scalar field theory is non linear? What will be the associated interaction potential of that equation?
-1
votes
1answer
144 views
Scalar field lagrangian and potential
This question is a continuation of this Phys.SE post.
Scalar field theory does not have gauge symmetry, and in particular, $\phi\to\phi−1$ is not a gauge transformation. but why?
and
I want see the ...
2
votes
2answers
137 views
Does a constant factor matter in the definition of the Noether current?
This is a very basic Lagrangian Field Theory question, it is about a definition convention. It takes much more time to typeset it than answering, but here it is:
Consider a field Lagrangian with only ...
1
vote
2answers
111 views
In Noether's theorem, what is a “classical solution of the equations of motion”?
I'm reading a book which states that:
for each generator of a global symmetry transformation, there is a
current $j^{\mu}_{a}$ which, when evaluated on a classical solution
of the equations of ...
1
vote
0answers
52 views
relevant 4-dimensional theory with interacting vector field
A simple langragian that gives the simplest interaction is $\mathcal{L}=(\partial\phi)^2+(m\phi)^2$ where $m$ is some constant. Does anyone know of theory in four dimensions which is physically ...
9
votes
1answer
173 views
Lagrangian for Goldstone mode + topological excitation
The XY-model Hamiltonian is the following,
$${\cal H}~=~-J\sum_{\langle i,j\rangle} \cos (\theta_i -\theta_j).$$
The Goldstone mode corresponds to term $(\nabla \theta)^2$ in the effective ...
8
votes
4answers
231 views
What makes an equation an 'equation of motion'?
Every now and then, I find myself reading papers/text talking about how this equation is a constraint but that equation is an equation of motion which satisfies this constraint.
For example, in the ...
1
vote
2answers
198 views
Partial derivative of Lagrangian density for vector field
The lagrangian density of a massless vector field is
$ \mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$, where $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$
Expanding out gives
...
4
votes
1answer
368 views
Deriving the action and the Lagrangian for a free particle in Relativistic mechanics
My question relates to
Landau, Classical Theory of Field, Chapter 2 - Relativistic Mechanics, paragraph 8 - The principle of least action.
As stated there, To determine the action integral for a ...
2
votes
2answers
1k views
Deriving Lagrangian density for electromagnetic field
In considering the (special) relativistic EM field, I understand that assuming a Lagrangian density of the form
$$\mathcal{L} =-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{1}{c}j_\mu A^\mu$$
and ...
9
votes
4answers
263 views
Is the Lagrangian of a quantum field really a 'functional'?
Weinberg says, page 299, The quantum theory of fields, Vol 1, that
The Lagrangian is, in general, a functional $L[\Psi(t),\dot{\Psi}(t)$], of a set of generic fields $\Psi[x,t]$ and their time ...
8
votes
4answers
472 views
Quantum mechanics as classical field theory
Can we view the normal, non-relativistic quantum mechanics as a classical fields?
I know, that one can derive the Schrödinger equation from the Lagrangian density
$${\cal L} ~=~ \frac{i\hbar}{2} ...
1
vote
1answer
124 views
Question on 1st order Lagrangian Derivation in Faddeev-Jackiw Formalism
I'm looking at this reference (sorry it's a postscript file, but I can't find a pdf version on the web. This paper describes a similar procedure).
The topic is the Faddeev-Jackiw treatment of ...
3
votes
3answers
289 views
Calculating lagrangian density from first principle
In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle.
16
votes
1answer
211 views
Why does charge conservation due to gauge symmetry only hold on-shell?
While deriving Noether's theorem or the generator(and hence conserved current) for a continuous symmetry, we work modulo the assumption that the field equations hold. Considering the case of gauge ...
11
votes
3answers
1k views
7
votes
1answer
341 views
What corresponds to this Lagrangian density?
Is there a physical example of a field that would have the following Lagrangian density
$$
L= \sqrt{1+\phi_x^2 +\phi_y^2+\phi_z^2}
$$
where the subscripts denote partial derivatives and $\phi$ is a ...
5
votes
1answer
270 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 ...
