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6
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1answer
252 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 ...
6
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0answers
196 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 ...
5
votes
3answers
380 views

Meaning of kinetic part in the Lagrangian density?

What is the physical meaning of the kinetic term in the classical scalar field Lagrangian $$\mathcal{L}_{kin}~=~\frac{1}{2}(\partial_\mu\phi)(\partial^\mu\phi)~?$$ It gives how does the field change ...
5
votes
1answer
275 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 ...
5
votes
1answer
1k 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 ...
5
votes
1answer
313 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 ...
5
votes
2answers
527 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 ...
5
votes
1answer
114 views
+50

How do creation operators change with time in an interacting theory?

When studying the quantization of a field theory with free fields, the creation operators $a^\dagger(k)$ are independent of time. In an interacting theory, they are time-dependant, and therefore ...
5
votes
5answers
256 views

Euler-Lagrange equation for continuous systems

I'm having a little trouble with wrapping my head around a part of a method which is fairly 'new' in some fashions to me. I imagine it should be fairly obvious, but I am not seeing something at the ...
5
votes
1answer
318 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 ...
5
votes
1answer
250 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 ...
5
votes
2answers
559 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) ...
5
votes
1answer
62 views

How can one (formally) determine the particle content of a free field theory?

Here's my question: Suppose I'm given a free field theory, where my fields are functions $\phi:\mathbb{R}^4 \rightarrow V$, and the equations of motion are a system of linear Lorentz-invariant ...
5
votes
2answers
147 views

Energy and momentum as partial derivatives of on-shell action in field theory

According to L&L, if we fix the initial position of a particle at a given time and consider the on-shell action as a function of the final coordinates and time, $S(q_1, \ldots, q_n, t)$, then... ...
5
votes
0answers
42 views

Spin-dependence of the directionality of dipole radiation

I am interested in understanding how and whether the transformation properties of a (classical or quantum) field under rotations or boosts relate in a simple way to the directional dependence of the ...
5
votes
0answers
72 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 ...
5
votes
0answers
380 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 ...
4
votes
3answers
123 views

Complex Dirac field in antiparticle description

I understand that the Dirac equation has negative and positive sets of solutions and this contributes to its quantization by a superposition of two Fourier modes represented as creation and ...
4
votes
4answers
1k 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
278 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 ...
4
votes
1answer
459 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 ...
4
votes
2answers
146 views

What guarantees the existence of unitary operators implementing Lorentz Transformations?

This should be a very basic question. In introductory QFT books, often one of the first things we see is the following claim: for every Lorentz transformation $\Lambda$, we can associate an unitary ...
4
votes
2answers
646 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 ...
4
votes
1answer
792 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 ...
4
votes
1answer
295 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 $$ ...
4
votes
1answer
75 views

Total derivative in action of the field theory

Consider a classical field theory. When applying the least action I see that a term is considered total derivative. We say that $$\int \partial_\mu (\frac {\partial L}{\partial(\partial_\mu ...
4
votes
1answer
118 views

Conceptual question about field transformation

(c.f Conformal Field Theory by Di Francesco et al, p39) From another source, I understand the mathematical derivation that leads to eqn (2.126) in Di Francesco et al, however conceptually I do not ...
4
votes
1answer
455 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
601 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 ...
4
votes
1answer
155 views

Spontaneous Symmetry Breaking

In Spontaneous symmetry breaking we have got that, a field $$\phi= \pm \sqrt{\frac{-m^2}{\lambda}}.$$ Now in order to get the unstable minima we need to guess the mass $m^2 <0 $. But can mass be ...
4
votes
1answer
159 views

Non-relativistic limit in a Lagrangian density

What criteria should I consider when determining the non-relativistic limit of a Lagrangian density? For example, how would I take the non-relativistic limit of the following Lagrangian density: ...
4
votes
1answer
122 views

Definition of vacuum in field theory; Connection between the classical definition and the connection to QFT

I am a bit confused by what is defined to be a vacuum in field theory. Classically a vaccum state is defined to be the state where the field sits at some minima of the potential $\frac{\partial ...
4
votes
2answers
263 views

Mean field theory = large-N approximation?

Wikipedia entry of 1/N expansion (or 't Hooft large-N expansion) mentions that It (large-N) is also extensively used in condensed matter physics where it can be used to provide a rigorous basis ...
4
votes
1answer
174 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 ...
4
votes
1answer
570 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 ...
4
votes
1answer
102 views
+50

Cut-off Regularisation and Renormalisation in Scalar Field Theory, Deriving the Cutoff Independent Physical Mass

I'm having trouble reproducing Equation 42: \begin{equation}\tag{1} m^{2}_{\text{phys}}= m^{2}_{r} + m^{2}_{r} \tilde{\lambda} \text{log} \left( \dfrac{m^{2}_{r}}{\mu^{2}} \right) \end{equation} ...
4
votes
2answers
95 views

Non-local structure of field theory

Can someone explain what is non-local structure of field theory? I know you cannot have $\phi(x) \phi(y)$ term in Lagrangian which indicates the non-locality. However, why I cannot have the non-local ...
4
votes
1answer
217 views

Noether's Theorem in Field Theory

This question is regarding Noether's Theorem in general, but also in the application to an example. The example is: Find the conserved current for the Lagrangian ...
4
votes
3answers
425 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.
4
votes
0answers
104 views

One more time about Nordstrom theory

Wikipedia says that Nordstrom theory with equations of motion of the test particle $$\tag{1} \frac{d (\varphi u_{\alpha})}{d \tau} = \partial_{\alpha} \varphi $$ and field equation $$\tag{2} \varphi ...
3
votes
1answer
218 views

Which transformations *aren't* symmetries of a Lagrangian?

As far as I understand, Noether's theorem for fields works, as explained in David Tong's QFT lecture notes (page 14) for example, by saying that a transformation $\phi(x) \mapsto \phi(x) + \delta \phi ...
3
votes
4answers
815 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
1answer
155 views

Definition of Local Function

Now a days I am studying Srednicki's QFT book. In its third chapter it is written that Any local function of φ(x) is a Lorentz scalar, [...] . Now my question is: What is a local function?
3
votes
1answer
698 views

Need for a side book for E.Soper`s Classical Theory Of Fields.

I am reading now E Soper Classical Theory Of Fields now and sometimes it is very hard to follow the equations.So I need a side book to read it comfortably.Landau`s book is not helping as its content ...
3
votes
2answers
158 views

Classical Field Theory - Continuum limit in forming the Lagrangian density and the elasticity modulus

I have been looking at taking the continuum limit for a linear elastic rod of length $l$ modeled by a series of masses each of mass $m$ connected via massless springs of spring constant $k$. The ...
3
votes
1answer
272 views

Why do we assume that Dirac spinor $\Psi$ describe the particle, not the field?

It is a well-known fact that Klein-Gordon scalar $\Psi(x)$, $$ (\partial^{2} + m^2) \Psi (x) = 0 $$ as well as 4-vector $A_{\mu}(x)$, $$ (\partial^{2} + m^{2})A_{\mu} = 0,\quad ...
3
votes
1answer
400 views

What exactly is the connection between the Jacobi and Bianchi identities

While reviewing some basic field theory, I once again encountered the Bianchi identity (in the context of electromagnetism). It can be written as $$\partial_{[\lambda}\partial_{[\mu}A_{\nu]]}=0$$ ...
3
votes
3answers
233 views

Are Field Lines an accurate depiction of reality?

Field lines are used for explaining a wide variety of phenomenon. But is it really an accurate depiction of reality? Is it more accurate to imagine a field in a different manner. For instance, using ...
3
votes
1answer
81 views

Lagrangian description of Brownian motion?

I'm interested in the existence of a Lagrangian field theory description of Bronwnian motion, does such a thing exist? Given a particle of some spin $\sigma$, which has a Lagrangian associated with ...
3
votes
2answers
594 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 ...