Questions tagged [field-theory]

For questions where the dynamical variables are fields, that is, functions of several variables (typically, one time coordinate and several space coordinates). Comprises both classical field theory and quantum field theory. Use this tag when the question applies to both classical and quantum phenomena. Otherwise, use the specific tag instead.

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6
votes
2answers
996 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 ...
7
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3answers
1k views

Is String Theory a Field Theory?

Is String Theory a Field or Quantum Mechanical Theory of the String rather than a Particle? I should know this having studied this for a term, but we jumped into the deep end, without really ...
2
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1answer
251 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 ...
9
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1answer
2k 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 ...
37
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1answer
2k 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 ...
5
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1answer
1k 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 ...
17
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2answers
7k 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 ...
9
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4answers
1k 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
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1answer
327 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 ...
22
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2answers
2k views

Wick rotation and spinors

I am quite familiar with use of Wick rotations in QFT, but one thing annoys me: let's say we perform it for treating more conveniently (ie. making converge) a functional integral containing spinors; ...
14
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5answers
3k 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} (\...
2
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1answer
166 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 ...
6
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0answers
254 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 ...
6
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1answer
2k 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: ...
2
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1answer
377 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 ...
74
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3answers
11k views

Differentiating Propagator, Green's 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 ...
5
votes
1answer
410 views

Is the long range neutron-antineutron interaction repulsive or attractive?

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 $E=-\...
6
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3answers
1k 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
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1answer
1k 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 ...
17
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3answers
3k views

Why can't General Relativity be written in terms of physical variables?

I am aware that the field in General Relativity (the metric, $g_{\mu\nu}$) is not completely physical, as two metrics which are related by a diffeomorphism (~ a change in coordinates) are physically ...
5
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2answers
4k 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 ...
73
votes
10answers
8k 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 me ...
2
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2answers
332 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 ...
4
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1answer
126 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 ...
1
vote
1answer
690 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 ...
2
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1answer
280 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 $\frac{g}{2}\left(\...
5
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2answers
1k 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) $$\square=...
14
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1answer
869 views

Could this model have soliton solutions?

We consider a theory described by the Lagrangian, $$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$ The corresponding field equations are, $$(i\...
21
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1answer
2k 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 ...
5
votes
1answer
700 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
3answers
1k 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 theory?...
15
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1answer
331 views

6d Massive Gravity

Massive gravity (with a Fierz-Pauli mass) in 4 dimensions is very well-studied, involving exotic phenomena like the van Dam-Veltman-Zakharov (vDVZ) discontinuity and the Vainshtein effect that all ...
10
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1answer
3k 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 ...
20
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3answers
1k views

Does 4D ${\cal N} = 3$ supersymmetry exist?

Steven Weinberg's book "The Quantum Theory of Fields", volume 3, page 46 gives the following argument against ${\cal N} = 3$ supersymmetry: "For global ${\cal N} = 4$ supersymmetry there is just ...
33
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5answers
6k views

Why are infinite order Lagrangians called 'non-local'?

And in what sense are they 'non-local'?
9
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1answer
641 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 ...
13
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5answers
620 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 ...
112
votes
9answers
31k 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 ...
10
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2answers
442 views

Does Noether's theorem also give rise to quantities conserved over space?

Noether's theorem gives rise to quantities that are conserved over time. But does it also give rise to quantities that are conserved over space?
7
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1answer
486 views

What corresponds to this Lagrangian density?

Is there a physical example of a field that would have the following Lagrangian density $$ L= \sqrt{1+\phi_x^2 +\phi_y^2+\phi_z^2} $$ where the subscripts denote partial derivatives and $\phi$ is a ...
8
votes
2answers
470 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 $F^{...
8
votes
3answers
1k 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 ...
7
votes
2answers
1k views

Fields and Newton's Third Law

I'm studying basic physics. I'm using the text available at http://www.anselm.edu/internet/physics/cbphysics/downloadsI.html. It develops the universal law of gravitation by postulating the existence ...
5
votes
1answer
438 views

formal framework for talking about 'minimal couplings'

usually on physical theories one would have Lagrangians or Hamiltonians with multiple fields; say, a vector $A_{\mu}$ and a scalar $\phi$ and one would postulate ad hoc a coupling between the fields ...
18
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4answers
2k 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 ...
5
votes
1answer
991 views

Einstein's Field equations and impulse-energy tensor

I premise that I haven't yet studied General Relativity, but in Relativistic Electrodymaics I have knowed impulse-energy tensor of Electromagnetic Field. I know in Einstein's equations there is ...
20
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5answers
5k views

What is the difference between a complex scalar field and two real scalar fields?

Consider a complex scalar field $\phi$ with the Lagrangian: $$L = \partial_\mu\phi^\dagger\partial^\mu\phi - m^2 \phi^\dagger\phi.$$ Consider also two real scalar fields $\phi_1$ and $\phi_2$ with ...
56
votes
4answers
21k views

Why correlation functions?

While this concept is widely used in physics, it is really puzzling (at least for beginners) that you just have to multiply two functions (or the function by itself) at different values of the ...
11
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1answer
6k views

The Euler-Lagrange equation in special relativity

How can I derive the Euler-Lagrange equations valid in the field of special relativity? Specifically, consider a scalar field.
7
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3answers
4k 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 field ...