The field-theory tag has no wiki summary.
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
3answers
287 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.
3
votes
1answer
91 views
Is the force between solitons with same charge always repulsive?
I know the one-dimensional case in which the force is proportional to $e^{-R}$ and the force is attractive for solitons with opposite charge and repulsive for solitons with same charge. I was ...
3
votes
1answer
319 views
What is / are the primary criticism(s) against Einstein-Cartan-Evans field theory?
What is / are the primary criticism(s) against Einstein-Cartan-Evans (ECE) field theory?
On Wikipedia the references provided were: arXiv:physics/0607186, MR2372785 (2008j:83049b), MR2218579 ...
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
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 ...
2
votes
2answers
162 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 ...
2
votes
1answer
195 views
Texts on field theory in classical physics
I need a very good text on field theory and it should provide good understanding of why this concept cant be ignored?I only need that text which will tell me how field theory is an integral part of ...
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 ...
2
votes
3answers
238 views
Massless limit of the Klein-Gordon propagator
I am working with the propagator associated to the Klein-Gordon equation, as derived in "Quantum Physics a functional integral point of view", James Glimm, Arthur Jaffe or as derived here: ...
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?
2
votes
2answers
355 views
Field theory:functional derivative involving Fourier Transform
I have to solve the following functional derivative
$$
\frac{\delta}{\delta \Lambda(\mathbf{x})}\log[A-\mathbf{k}^2\Lambda(\mathbf{k})]
$$
where $\Lambda(\mathbf{k})$ is the Fourier transform of ...
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 ...
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 ...
2
votes
1answer
108 views
Crushing a magnetic field
What would happen if you crushed a magnetic field to an ever decreasing size?
Thanks.
EDIT:
How small could the field possibly go? Is there a limit on how small it could get?
Is there a maximum ...
2
votes
1answer
173 views
How to perform a scale (invariance) transformation?
According to this wikipedia article in the $\phi^4$ section, the equation
$$\frac{1}{c^2}\frac{∂^2}{∂t^2}\phi(x,t)-\sum_i\frac{∂^2}{∂x_i^2}\phi(x,t)+g\ \phi(x,t)^3=0,$$
in 4 dimensions is invariant ...
2
votes
2answers
635 views
Proof that Energy Momentum Tensor of Scalar Field Theory satisfies Weak Energy Condition
It's a question on Sean Carroll's Spacetime and Geometry, where we are supposed to prove that the energy momentum tensor of scalar field theory satisfies Weak Energy Condition (WEC). The energy ...
2
votes
2answers
126 views
Inertial Mass of a scalar field
Does it make sense to talk of the inertial mass of a scalar field? By the equivalence principle, it must be equal to its gravitational mass. We know that the scalar field contributes towards the ...
2
votes
1answer
144 views
Classical scalar field correlation function
How should I interpret the left-hand side of this expression
$$ \langle \phi(k)\phi(-k) \rangle ~=~ \frac{\mathrm{i}}{k^2 -m^2},$$
which appears on pg. 3 of Matt Strassler's TASI 2001 notes:
...
2
votes
2answers
216 views
Counting degrees of freedom in presence of constraints
In a $N$ dimensional phase space if I have $M$ 1st class and $S$ 2nd class constraints, then I have $N-2M-S$ degrees of freedom in phase space. How can I calculate the degrees of freedom in ...
2
votes
1answer
103 views
What's the meaning of the coupling change after a renormalization (in the 1-dim Ising Model)?
What does it mean that after the theory (1-dim Ising model here, but the question is general) is renormalized one time and $g_i\rightarrow g_i'$, that the couplings are weaker, even if the theory ...
2
votes
1answer
214 views
Is Thirring model a particular case of Gross model?
Look at this: http://en.wikipedia.org/wiki/Gross-Neveu_model
Wikipedia sais "When N=1 it reduces to the integrable Thirring model". but the aditional term in thirring model is ...
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 ...
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?
2
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0answers
63 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 ...
1
vote
4answers
146 views
Cubic term in gauge theories
In ordinary classical gauge theories the term $-\frac{1}{2}\mathrm{Tr}(F_{\mu\nu}F^{\mu\nu})=-\frac{1}{4}F^a_{\mu\nu}F_a^{\mu\nu}$ in the Lagrangian is completely natural. A somehow rare term would be ...
1
vote
1answer
69 views
Do field and potential energy always come together?
Is energy directly due to a field always potential energy?
Is potential energy always due to a field?
From the two Wikipedia links:
a field is a physical quantity that has a value for each ...
1
vote
1answer
259 views
Understanding P-, CP-, CPT-violation etc. in field theory and in relation to the principle of relativity
I can never get my head around the violations of $P-$, $CP-$, $CPT-$ violations and their friends. Since the single term "symmetry" is so overused in physics and one has for example to watch out and ...
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 ...
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 ...
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
1answer
117 views
Is it possible to describe the entire universe with the behavior of an $\mathbb{R}^n$ field?
Suppose every phenomena in this universe (of course most are reducible to some particular general ideal ones - basically I'm talking about those!) could be described as ...
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 ...
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 ...
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
$$x(t)=x(0)\cos(\omega_0 t)+C ...
1
vote
0answers
52 views
relevant 4-dimensional theory with interacting vector field
A simple langragian that gives the simplest interaction is $\mathcal{L}=(\partial\phi)^2+(m\phi)^2$ where $m$ is some constant. Does anyone know of theory in four dimensions which is physically ...
1
vote
2answers
198 views
Partial derivative of Lagrangian density for vector field
The lagrangian density of a massless vector field is
$ \mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$, where $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$
Expanding out gives
...
1
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0answers
46 views
Limit of the scalar field, and potential for a soliton ( finite energy, non dissipative) solution
I want to prove that the the scalar field of the yang-mills lagrangian tends to some constant value which is a function of theta at infinity and that this value is a zero of the potential, when we ...
0
votes
2answers
53 views
Derrick’s theorem
Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$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
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 ...
0
votes
1answer
103 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
$$S=\int d^d\! x ...
0
votes
1answer
77 views
Oscillon and soliton
I want to know the major difference between oscillon and soliton in terms of radiating energy with respect to time and position. And what about their localization?
0
votes
1answer
85 views
sine-Gordon equation
I have derived a solition equation (2 dimensions) from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{1}$$
and also I have got sine-Gordon equation for solition
...
0
votes
1answer
52 views
Why do fields decrease with distance? [duplicate]
For example, electric, gravitational field decreases with $1/r^2$. Is it like decrease of energy of an object when goes it is moving with friction/air drag etc?
Does it mean that field's strength is ...
0
votes
2answers
152 views
Difficulties with bra and ket notation
I have problem in understanding equation (1.23), I croped this image from Mark_Srednicki "Quantum field theory". Can anyone show me the reason for the equation (1.23)?
0
votes
1answer
84 views
Two similar questions related to analytic continuation of a complex variable and its conjugate
See the scan attached below. Brown, in his QFT book, argues a certain way to do an integral. I understand that 1.8.13 or equivalently 1.8.14 can be performed once analytic continuation is done. I ...
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0answers
22 views
Counting the modes of the vector potential in a coulomb gauge
With a view to quantising the EM field, consider a classical free field in the absence of charge and currents, we can take a coulomb gauge, $\phi=0, \partial_kA_k=0$. The physical fields in terms of ...
0
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0answers
61 views
Derrick’s theorem(2)
Related post : Derrick’s theorem
Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) ...
0
votes
0answers
45 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 ...
