The field-theory tag has no wiki summary.
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1answer
192 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 ...
8
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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 ...
3
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3answers
235 views
Particles as a limit of classical field theory
A common academic exercise has been to show that classical mechanics is a limit of quantum mechanics, usually by putting $\hbar \rightarrow 0$.
Similarly is it possible to show that a limit to field ...
1
vote
4answers
145 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 ...
2
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2answers
353 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 ...
8
votes
4answers
468 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
$${\cal L} ~=~ \frac{i\hbar}{2} ...
1
vote
2answers
197 views
Partial derivative of Lagrangian density for vector field
The lagrangian density of a massless vector field is
$ \mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$, where $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$
Expanding out gives
...
2
votes
1answer
96 views
What's the difference between background field and dynamical gauge field?
Dynamical gauge fields are assumed to be able to respond to sources.
What's the difference in the Lagrangians between a background field and a dynamical field?
5
votes
1answer
128 views
Electromagnetic 4-potential and basic index contraction
I'm trying to learn about relativistic electrodynamics on my own, and I am struggling with derivatives of the 4-potential and index (Einstein) notation.
I think I understand expressions such as ...
4
votes
1answer
164 views
Quantum Field Theory: why fields are equal to zero on the boundary?
One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is
$$
\phi(x)=0\,\text{on the boundary}
$$
and this is widely used in many situations ...
3
votes
4answers
438 views
Are the field lines the same as the trajectories of a particle with initial velocity zero
Is it true that the field lines of an electric field are identical to the trajectories of a charged particle with initial velocity zero? If so, how can one prove it?
The claim is from a german ...
4
votes
1answer
364 views
Deriving the action and the Lagrangian for a free particle in Relativistic mechanics
My question relates to
Landau, Classical Theory of Field, Chapter 2 - Relativistic Mechanics, paragraph 8 - The principle of least action.
As stated there, To determine the action integral for a ...
4
votes
1answer
248 views
What is the essence of BCFW recursion techniques?
I have recently briefly read about new methods as the Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion method.
Can anybody please tell me about the essence of it?
What does it mean for the ...
2
votes
1answer
144 views
Classical scalar field correlation function
How should I interpret the left-hand side of this expression
$$ \langle \phi(k)\phi(-k) \rangle ~=~ \frac{\mathrm{i}}{k^2 -m^2},$$
which appears on pg. 3 of Matt Strassler's TASI 2001 notes:
...
2
votes
1answer
214 views
Is Thirring model a particular case of Gross model?
Look at this: http://en.wikipedia.org/wiki/Gross-Neveu_model
Wikipedia sais "When N=1 it reduces to the integrable Thirring model". but the aditional term in thirring model is ...
1
vote
1answer
117 views
Is it possible to describe the entire universe with the behavior of an $\mathbb{R}^n$ field?
Suppose every phenomena in this universe (of course most are reducible to some particular general ideal ones - basically I'm talking about those!) could be described as ...
3
votes
2answers
173 views
Linearizing Gravity to ${\cal O}(h^3)$
I've seen the action of linearized gravity in many places. We basically have
$${\cal L} \sim \frac{1}{G_N}\left( - \frac{1}{2}h^{\alpha\beta} \Box h_{\alpha\beta} + \frac{1}{4} h \Box h + {\cal ...
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 ...
2
votes
2answers
215 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 ...
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9answers
2k views
What is a field, really?
There was a reason why I constantly failed physics at school and university, and that reason was, apart from the fact I was immensely lazy, that I mentally refused to "believe" more advanced stuff ...
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 ...
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
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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 ...
3
votes
1answer
152 views
Does spontanous symmetry breaking affect Noethers theorem?
Does spontanous symmetry breaking affect the existence of a conserved charge?
And how does depend on whether we look at a classical or a quantum field theory (e.g. the weak interacting theory)?
...
5
votes
3answers
355 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 ...
13
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4answers
1k views
History of Electromagnetic Field Tensor
I'm curious to learn how people discovered that electric and magnetic fields could be nicely put into one simple tensor.
It's clear that the tensor provides many beautiful simplifications to the ...
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 ...
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 ...
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 ...
5
votes
2answers
318 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 ...
4
votes
1answer
353 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 ...
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 ...
16
votes
1answer
532 views
Can lightning be used to solve NP-complete problems?
I'm a MS/BS computer science guy who is wondering about why lightning can't (or can?) be used to solve NP complete problems efficiently, but I don't understand the physics behind lightning, so I'm ...
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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} - ...
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 ...
4
votes
1answer
203 views
U(1) Charged Fields
I don't quite understand what is actually meant by a field charged under a $U(1)$ symmetry.
Does it mean that when a transformation is applied the field transforms with an additional phase? More ...
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3answers
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3
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2answers
364 views
Are there solitary waves in $\phi^4$ theory in 3+1 dimensions?
In 3+1 dimensions with signature +1 -1 -1 -1,
$$ \mathcal{L}= \frac{1}{2}\partial^\mu\phi\partial_\mu\phi -\phi^2/2 -\phi^4/4$$
field equation: $$\square\phi+\phi+\phi^3=0$$ (check this)
...
3
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1answer
246 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
660 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 ...
2
votes
2answers
627 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 ...
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.
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 ...
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 ...
5
votes
3answers
380 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 ...
6
votes
1answer
438 views
The equipartition theorem in momentum space
Motivated by the answers to this question on turbulence, I'm interested in an explanation and/or derivation/reference of the equipartition theorem in momentum space. To formulate it as a question:
...
1
vote
1answer
123 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
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
$$ ...
9
votes
4answers
405 views
Why must the field equations be differential?
In Landau–Lifshitz's Course of Theoretical Physics, Vol. 2 (‘Classical Fields Theory’), Ch. IV, § 27, there is an explanation why the field equations should be linear differential equations. It goes ...
