The field-theory tag has no wiki summary.
9
votes
1answer
159 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 ...
4
votes
1answer
123 views
Noether's identities
I have some questions about the Noether's second theorem (generally not covered by field theory books):
What is the most general Noether identity for (classical) field theories?
Why are Noether ...
0
votes
0answers
19 views
Counting the modes of the vector potential in a coulomb gauge
With a view to quantising the EM field, consider a classical free field in the absence of charge and currents, we can take a coulomb gauge, $\phi=0, \partial_kA_k=0$. The physical fields in terms of ...
1
vote
2answers
48 views
Does spatial coupling prohibit resonances due to an external source field?
The harmonic oscillator coupled to a sinodial external source
$$\tfrac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$
has the solution
$$x(t)=x(0)\cos(\omega_0 t)+C ...
0
votes
1answer
75 views
Higher order covariant Lagrangian
I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
0
votes
0answers
61 views
Derrick’s theorem(2)
Related post : Derrick’s theorem
Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) ...
-3
votes
0answers
39 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
$$V(\phi)= ...
0
votes
1answer
56 views
Vortex in D dimensions soliton
let us consider
the two-dimensional configuration shown in Fig. 3.1a. The lengths of the arrows
represent the magnitude of φ, while their directions indicate the orientation in
the $φ_1 -φ_2$ plane. ...
0
votes
2answers
52 views
Derrick’s theorem
Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
0
votes
1answer
83 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
44 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 ...
2
votes
3answers
276 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 ...
-3
votes
0answers
52 views
Is it possible that gravity is merely a field effect of magnetism? [closed]
In my world, the Universe is expanding, the galaxies orbit each other, the stars orbit the centers of galexies, the planets orbit the stars and the moons orbit the planets. But when an apple falls,... ...
-1
votes
1answer
112 views
Double- well potential and Mexican potential
Is double well potential related to Maxican hat potential?
I have found on Quantum Field Theory in a Nutshell
by A. Zee
He wrote the double well potential as : $V (φ) = (λ/4)(φ^ 2 − v^2)^2$.
Can ...
-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}$$
What I want to do is ...
0
votes
1answer
84 views
Comparing interaction potential in standard $ϕ^4 $theory
I am posting this question again because, Willie Wong asked me to do it. So it is a continuing post of the Interaction potential in standard ϕ4 theory.
I have been studying about solitions so I had ...
1
vote
1answer
103 views
Potential in Relativistic Scalar Field Theory
My intention is to establish a Soliton equation. I have cropped a page from Mark Srednicki page no 576.
I have understand the equation (92.1) but don't understand that how they guessed the ...
-3
votes
1answer
139 views
$\phi ^4$ theory explaining [closed]
In $φ^4$ theory we often write the Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$
If I want to write from the ...
6
votes
2answers
146 views
From Lagrangian to Hamiltonian in Fermionic Model
While going from a given Lagrangian to Hamiltonian for a fermionic field, we use the following formula. $$ H = \Sigma_{i} \pi_i \dot{\phi_i} - L$$ where $\pi_i = \dfrac{\partial L}{\partial ...
18
votes
7answers
856 views
Why are differential equations for fields in physics of order two?
What is the reason for the observation that across the board fields in physics are generally governed by second order (partial) differential equations?
If someone on the street would flat out ask ...
4
votes
0answers
40 views
The consistency conditions of constrained Hamiltonian systems
I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
0
votes
1answer
52 views
Why do fields decrease with distance? [duplicate]
For example, electric, gravitational field decreases with $1/r^2$. Is it like decrease of energy of an object when goes it is moving with friction/air drag etc?
Does it mean that field's strength is ...
-1
votes
1answer
65 views
How the nonlinear equation can be written like this?
We consider a scalar theory in a $1+D$ dimensional flat Minkowski
space-time, with a general self-interaction
potential, whose action can be written as
\begin{equation}
A=\int dt\, d^D\! x ...
0
votes
1answer
102 views
Interaction potential analysis from $\phi^4$ model
In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by
$$S=\int d^d\! x ...
0
votes
1answer
77 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?
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
votes
1answer
74 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
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 ...
-3
votes
1answer
229 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
151 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)?
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?
1
vote
2answers
110 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 ...
2
votes
0answers
62 views
Is a solution to the Klein-Gordon equation homeomorphic (or even diffeomorphic) to a solution of an equation with a different covariance group?
Consider some solution $\psi(x,t)$ to the linear Klein-Gordon equation: $-\partial^2_t \psi + \nabla^2 \psi = m^2 \psi$. Up to homeomorphism, can $\psi$ serve as a solution to some other equation ...
0
votes
0answers
47 views
What is the difference between Mean Field Theory and Effective Medium Theory?
I understand that Effective Medium Theory (EMT) is a kind of Mean Field Theory (MFT), but I am unclear about the distinction.
What are the defining characteristics of a Mean Field Theory?
What ...
9
votes
4answers
262 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 ...
5
votes
2answers
196 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 ...
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 ...
5
votes
0answers
81 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 ...
2
votes
2answers
195 views
Pair production - mathematically?
Allover the web i am only seeing a statement similar to this:
Pair production is not possible in vaccum, 3rd particle is needed so
that conservation of momentum holds.
Well noone out of many ...
16
votes
1answer
208 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 ...
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
166 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
4answers
399 views
First class and second class constraints
Hello I am working on a project that involves the constraints. I checkout the paper of Dirac about the constraints as well as some other resources. But still confuse about the first class and second ...
3
votes
0answers
85 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:
...
15
votes
1answer
1k views
Differentiating Propagator, Greens function, Correlation function, etc
For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most ...
0
votes
1answer
84 views
Two similar questions related to analytic continuation of a complex variable and its conjugate
See the scan attached below. Brown, in his QFT book, argues a certain way to do an integral. I understand that 1.8.13 or equivalently 1.8.14 can be performed once analytic continuation is done. I ...
2
votes
2answers
161 views
Is the artificial gauge field a gauge field?
The so-called artificial gauge fields are actually the Berry connection. They could be $U(1)$ or $SU(N)$ which depends on the level degeneracy.
For simplicity, let's focus on $U(1)$ artificial gauge ...
5
votes
0answers
201 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 ...
