The field-theory tag has no wiki summary.
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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
$$x(t)=x(0)\cos(\omega_0 t)+C ...
4
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1answer
107 views
Noether's identities
I have some questions about the Noether's second theorem (generally not covered by field theory books):
What is the most general Noether identity for (classical) field theories?
Why are Noether ...
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1answer
75 views
Higher order covariant Lagrangian
I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
-1
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1answer
108 views
Double- well potential and Mexican potential
Is double well potential related to Maxican hat potential?
I have found on Quantum Field Theory in a Nutshell
by A. Zee
He wrote the double well potential as : $V (φ) = (λ/4)(φ^ 2 − v^2)^2$.
Can ...
9
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0answers
141 views
Lagrangian for Goldstone mode + topological excitation
The XY-model Hamiltonian is the following,
$${\cal H}~=~-J\sum_{\langle i,j\rangle} \cos (\theta_i -\theta_j).$$
The Goldstone mode corresponds to term $(\nabla \theta)^2$ in the effective ...
8
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0answers
436 views
Could this model have soliton solutions?
$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$
Field equation $(i\gamma^\mu\partial_\mu-m+g\bar{\Psi}\Psi)\Psi=0$
Could this model have soliton ...
5
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0answers
81 views
Auxiliary fields in supersymmetry
I know that auxiliary fields can be used to close the supersymmetry algebra in case the bosonic and fermionic on-shell degrees of freedom do not match. Could somebody please elaborate on this concept ...
5
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0answers
201 views
Gaussian Integrals : Functional determinant expressed as a trace
Be $A_{ij}$ a symmetric matrix. Then I can easily write
$$
\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 ...
5
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0answers
170 views
Are there known turbulent nonlinear equations where the cascade is a thermal gradient?
In a recent answer (here: The equipartition theorem in momentum space ), I suggested that if you have an appropriate first order equation (in the answer I used a second order equation, but it is more ...
4
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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 ...
3
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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:
...
2
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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?
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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 ...
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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 ...
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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 ...
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0answers
46 views
Limit of the scalar field, and potential for a soliton ( finite energy, non dissipative) solution
I want to prove that the the scalar field of the yang-mills lagrangian tends to some constant value which is a function of theta at infinity and that this value is a zero of the potential, when we ...
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0answers
14 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 ...
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0answers
60 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 $$L= \frac{1}{2} G_{ab}(\phi) ...
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0answers
44 views
Domain wall and kink solutions from solitions equations
A general solition equation can be obtaion from scalar field theory $$\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 ...
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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 ...
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0answers
65 views
What is the potential of the field?
In field theory, the key word is the Lagrangian $L(\phi(x^{\mu}), \frac{\partial \phi (x^{\mu}) }{\partial x^\mu}) $.
The equations of motion can be written as $\frac{\partial L}{\partial \phi} - ...
