Tagged Questions
-3
votes
0answers
40 views
graph plotting for a solition function [closed]
I have got a solition equation
$$ \phi(x)= v\tanh\left[ \frac{m}{\sqrt 2} (x-x_0)\right]$$ where, $$m=v\sqrt\lambda$$
Now I need to visualize or simulate this function.
I know little about ...
-2
votes
0answers
52 views
Mass of classical kink [closed]
related post Solving the soliton equation without energy
The energy density of kink solution is
$$\epsilon(x)= \frac{1}{2}(\frac{d \phi}{dx})^2+ V(\phi)$$
where the potential
$$V(\phi)= ...
0
votes
0answers
61 views
Derrick’s theorem(2)
Related post : Derrick’s theorem
Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) ...
0
votes
2answers
53 views
Derrick’s theorem
Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
0
votes
1answer
56 views
Vortex in D dimensions soliton
let us consider
the two-dimensional configuration shown in Fig. 3.1a. The lengths of the arrows
represent the magnitude of φ, while their directions indicate the orientation in
the $φ_1 -φ_2$ plane. ...
0
votes
1answer
85 views
sine-Gordon equation
I have derived a solition equation (2 dimensions) from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{1}$$
and also I have got sine-Gordon equation for solition
...
0
votes
0answers
46 views
Domain wall and kink solutions from solitions equations
A general solition equation can be obtaion from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{92.6}$$
where $x_0$ is a constant of integration when we drived this ...
-1
votes
1answer
79 views
Symmetry breaking with Lagrangian
I have been studying the spontaneous symmetry braking from Zee (Quantum Field theory ) and found in the page 224, he wrote the lagrangian as
$$\mathcal{L}=
\frac{1}{2}\{
λ
(∂φ)^2 + μ^2φ^ 2\} − ...
1
vote
0answers
57 views
A fundamental equation for solitary wave and dimension analysis
According to the scalar Field theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$
What I want to do is ...
0
votes
1answer
84 views
Comparing interaction potential in standard $ϕ^4 $theory
I am posting this question again because, Willie Wong asked me to do it. So it is a continuing post of the Interaction potential in standard ϕ4 theory.
I have been studying about solitions so I had ...
-3
votes
1answer
140 views
$\phi ^4$ theory explaining [closed]
In $φ^4$ theory we often write the Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$
If I want to write from 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
65 views
How the nonlinear equation can be written like this?
We consider a scalar theory in a $1+D$ dimensional flat Minkowski
space-time, with a general self-interaction
potential, whose action can be written as
\begin{equation}
A=\int dt\, d^D\! x ...
0
votes
1answer
104 views
Interaction potential analysis from $\phi^4$ model
In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by
$$S=\int d^d\! x ...
0
votes
1answer
80 views
Oscillon and soliton
I want to know the major difference between oscillon and soliton in terms of radiating energy with respect to time and position. And what about their localization?
-3
votes
1answer
230 views
Creation and Annihilation operator [closed]
In this page I want to know, why the equation (1.32) introduced creation and annihilation operator. Please elaborate.
0
votes
2answers
152 views
Difficulties with bra and ket notation
I have problem in understanding equation (1.23), I croped this image from Mark_Srednicki "Quantum field theory". Can anyone show me the reason for the equation (1.23)?
-1
votes
1answer
143 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
0answers
39 views
Is Inflation modelled by a field?
If Inflation is modelled by a field - is this a classical field or a quantum field? If classical are there good reasons not to quantise it? What are the implications of such a quantisation?
5
votes
2answers
197 views
Why is the Yang-Mills gauge group assumed compact and semi-simple?
What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories? I'd think that these hypotheses lead to physically ...
5
votes
0answers
82 views
Auxiliary fields in supersymmetry
I know that auxiliary fields can be used to close the supersymmetry algebra in case the bosonic and fermionic on-shell degrees of freedom do not match. Could somebody please elaborate on this concept ...
3
votes
1answer
190 views
Local and Global Symmetries
Could somebody point me in the direction of a mathematically rigorous definition local symmetries and global symmetries for a given (classical) field theory?
Heuristically I know that global ...
1
vote
1answer
167 views
Lorentz Invariant Equation of Motion for Scalar Field
I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity.
Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
3
votes
0answers
86 views
Asymptotic limit of the two kink solution of the sine-gordon equation
I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as:
...
5
votes
0answers
203 views
Gaussian Integrals : Functional determinant expressed as a trace
Be $A_{ij}$ a symmetric matrix. Then I can easily write
$$
\int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx=
\sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log ...
2
votes
1answer
96 views
What's the difference between background field and dynamical gauge field?
Dynamical gauge fields are assumed to be able to respond to sources.
What's the difference in the Lagrangians between a background field and a dynamical field?
4
votes
1answer
165 views
Quantum Field Theory: why fields are equal to zero on the boundary?
One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is
$$
\phi(x)=0\,\text{on the boundary}
$$
and this is widely used in many situations ...
4
votes
1answer
250 views
What is the essence of BCFW recursion techniques?
I have recently briefly read about new methods as the Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion method.
Can anybody please tell me about the essence of it?
What does it mean for the ...
3
votes
1answer
196 views
When can a classical field theory be quantized?
Given a classical field theory can it be always quantized? Put in another way, Does there necessarily need to exist a particle excitation given a generic classical field theory? By generic I mean all ...
5
votes
3answers
359 views
Gauge fixing choice for the gauge field $A_0$
In many situations, I have seen that the the author makes a gauge choice $A_0=0$, e.g. Manton in his paper on the force between the 't Hooft Polyakov monopole.
Please can you provide me a ...
2
votes
1answer
319 views
Inverse square law in 2+1 dimensional universe from a Yukawa coupling?
There is a nice result that in 3+1 space time, a Yukawa coupling leads to an inverse square law force as the mass of the scalar field goes to zero. I was wondering what the corresponding force in a ...
5
votes
2answers
322 views
Winding number in the topology of magnetic monopoles
I am reading on magnetic monopoles from a variety of sources, eg. the Jeff Harvey lectures.. It talks about something called the winding $N$, which is used to calculate the magnetic flux. I searched ...
3
votes
1answer
248 views
QED BRST Symmetry
This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim:
"Consider QED ...
3
votes
2answers
667 views
What is a non linear $\sigma$ model?
What exactly is a non linear $\sigma$ model? In many books one can view many different types of non linear $\sigma$ models but I don't understand what is the link between all of them and why it is ...
4
votes
1answer
191 views
what is a kink-kink-meson vertex?
These are questions I have after reading the Rajaraman's book "Solitons and instantons". So I think you must have read the book if want to answer. And also know about quantum solitons.
Rajaraman ...
3
votes
1answer
138 views
Is the long range neutron-antineutron interaction repulsive?
I can model this interaction as Zee does in "Quantum field theory in a nutshell". In chapter I.4 section "from particle to force" he uses two delta functions for the source. The integral gives ...
3
votes
1answer
177 views
SU(2) yang-mills EOM
I'm just playing around tonight trying to better myself, but I'm having trouble with some indices on my yang-mills lagrangian. I have a gauge group $SU(2)$ and a field strength tensor
$$ ...
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.
8
votes
0answers
438 views
Could this model have soliton solutions?
$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$
Field equation $(i\gamma^\mu\partial_\mu-m+g\bar{\Psi}\Psi)\Psi=0$
Could this model have soliton ...
4
votes
1answer
354 views
About $\phi^4$ model
In many books the $\phi^4$ model can produce a topological soliton called kink. Are they right? In the case of sine-Gordon model you can have a topological soliton due to you can express the ...
3
votes
1answer
587 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 ...
11
votes
3answers
1k views
7
votes
1answer
364 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 ...
8
votes
2answers
321 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 ...
5
votes
3answers
381 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 ...
4
votes
2answers
847 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 ...
