Tagged Questions
0
votes
1answer
76 views
Derivation of Dirac equation using the Lagrangian density for Dirac field
How can I find Dirac equation using the Lagrangian density for Dirac field?
4
votes
2answers
86 views
Independent systems and Lagrangians
Definition 1:
The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
2
votes
1answer
67 views
Determinant for a coupled fluctuation Lagrangian
Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
0
votes
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
vote
0answers
40 views
Lagrangians for non-local equations of motion
Say I have a multicomponent field $X_a(x,t)$ such that I know it Fourier modes satisfy the following equation of motion,
$(\delta_{ab} \partial_t + \Omega_{ab}(t))X_b(k,t) = e^t \int \frac{d^3p ...
-1
votes
1answer
109 views
Lagrangian formulation for relativistic case
Lagrangian for a real scalar field:
$$\mathcal{L}=\frac{1}{2}\eta^{\mu \nu}\partial_{\mu}\phi\partial_{\nu}\phi-\frac{1}{2}m^2\phi^2 $$
Can someone simply drive me how can I write it from ...
-1
votes
1answer
144 views
Scalar field lagrangian and potential
This question is a continuation of this Phys.SE post.
Scalar field theory does not have gauge symmetry, and in particular, $\phi\to\phi−1$ is not a gauge transformation. but why?
and
I want see the ...
1
vote
1answer
192 views
What is the Lagrangian from which the Klein-Gordon equation is derived in QFT?
Is there a well-known Lagrangian that, writing the corresponding eq of motion, gives the Klein-Gordon Equation in QFT? If so, what is it?
What is the canonical conjugate momentum? I derive the same ...
4
votes
2answers
297 views
Lorentz invariance of the integration measure
This is regards to the lorentz invariance of a classical scalar field theory. We assume that the action which is $S= \int d^4 x \mathcal{L}$, is invariant under a Lorentz transformation. How do you ...
2
votes
1answer
175 views
Scalar Field Theory Decay/Scattering
I have a few questions related to the following interaction Lagrangian (no use of crossing symmetry in the following) involving the uncharged scalar $\chi$ and the charged scalar $\phi$:
...
7
votes
1answer
238 views
Lagrangian of 2D square lattice of point masses connected by springs
Zee's QFT book mentions the Lagrangian of a square 2D horizontal lattice of point masses, connected by springs, and considering only vertical displacements $q_{i}$, as
$ L = \frac{1}{2} ...
2
votes
4answers
304 views
Why the Hamiltonian and the Lagrangian are used interchangeably in QFT perturbation calculations
Whenever one needs to calculate correlation functions in QFT using perturbations one encounters the following expression:
$\langle 0| some\ operators \times \exp(iS_{(t)}) |0\rangle$
where, ...
2
votes
1answer
123 views
Relationship between local and global scaling (Weyl) symmetry
Theorem 5.1 on page 80 of this paper says that
Assuming that the matter fields satisfy their equations of motion, the matter field action is locally Weyl invariant if and only if the corresponding ...
2
votes
1answer
195 views
How to tell local and unlocal in QFT?
I'm taking QFT course in this term. I'm quite curious that in QFT by which part of the mathematical expression can we tell a quantity or a theory is local or unlocal.
4
votes
2answers
147 views
Kugo and Ojima's Canonical Formulation of Yang-Mills using BRST
I am trying to study the canonical formulation of Yang-Mills theories so that I have direct access to the $n$-particle of the theory (i.e. the Hilbert Space). To that end, I am following Kugo and ...
5
votes
2answers
200 views
Can auxiliary fields be thought of as Lagrange multipliers?
In the BRST formalism of gauge theories, the Lautrup-Nakanishi field $B^a(x)$ appears as an auxiliary variable
$$\mathcal{L}_\text{BRST}=-\frac{1}{4}F_{\mu\nu}^a F^{a\,\mu\nu}+\frac{1}{2}\xi B^a B^a + ...
5
votes
2answers
287 views
The Lagrangian in Scalar Field Theory
This is perhaps a naive question, but why do we write down the Lagrangian
$$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2}m^2\phi^2$$
as the simplest ...
4
votes
2answers
264 views
Gauge fixing and equations of motion
Consider an action that is gauge invariant. Do we obtain the same information from the following:
Find the equations of motion, and then fix the gauge?
Fix the gauge in the action, and then find the ...
3
votes
4answers
598 views
Lagrangian to Hamiltonian in Quantum Field Theory
While deriving Hamiltonian from Lagrangian density, we use the formula
$$\mathcal{H} ~=~ \pi \dot{\phi} - \mathcal{L}.$$
But since we are considering space and time as parameters, why the formula
...
3
votes
3answers
266 views
What is the difference between manifest Lorentz invariance and canonical Lorentz invariance?
I often read that the Lorentz symmetry is manifest in the path integral formulation but is not in the canonical quantization - what does this really mean?
3
votes
1answer
317 views
Noether current for the Yang-mills-higgs lagrangian
I am trying to calculate the Noether's current, more specifically, the energy density of the Yang-mills-Higgs Lagrangian. Please refer to the equations in the Harvey lectures on Magnetic Monopoles, ...
1
vote
2answers
283 views
Why is ${\partial^i}{\partial_i\phi}$ = ${\partial^i {\phi}}{\partial_i{\phi}}$?
This notation can be found on page 254 of Victor Stenger's Comprehensible Cosmos and in David Tong's Lectures on QFT (Equation 2.4 http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf), and in
EDIT: on ...
1
vote
2answers
263 views
M-theory no lagrangian?
Is there any formulated lagrangian (density) for M-theory? If not, why is there no lagrangian?
If not, is this related to many vacua existing?
Thnx.
2
votes
1answer
209 views
Spontaneous symmetry breaking and 't Hooft and Polyakov monopoles
What is spontaneous symmetry breaking from a classical point of view. Could you give some examples, using classical systems.I am studying about the 't Hooft and Polyakov magnetic monopoles solutions, ...
3
votes
1answer
248 views
Gauge-invariant field strength term in Yang-Mills Lagrangian
I am reading the chapter of non-abelian gauge invariance from Peskin and Schroeder. Why is the term $-\frac{1}{4}(L_{\mu\nu}^i)^{2} $ gauge invariant?
3
votes
2answers
327 views
The Faddeev-Popov Lagrangian
This is a non-abelian continuation of this QED question.
The Lagrangian for a non-abelian gauge theory with gauge group $G$, and with fermion fields and ghost fields included is given by
$$
...
9
votes
5answers
1k views
Why not using Lagrangian, instead of Hamiltonian, in non relativistic QM?
When we studied classical mechanics on the undergraduate level, on the level of Taylor, we covered Hamiltonian as well as Lagrangian mechanics.
Now when we studied QM, on the level of Griffiths, we ...
4
votes
2answers
183 views
Is the form of the Lagrangian relevant before the renormalization procedure?
In the renormalization procedure, is writing things like
$$\varphi=\sqrt{Z_{\varphi}}\ \varphi_R\ ,\ \ m_0^2=Z_m\ m_R^2\ ,\ \ g_0=Z_g \mu^{\epsilon}\ g_R$$
and
$$Z_i=1+\sum_{\nu=1}^\infty ...
3
votes
3answers
289 views
Calculating lagrangian density from first principle
In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle.
2
votes
1answer
148 views
Differentiation of the action functional
In the QFT book by Itzykson and Zuber, the variation of the action functional $I=\int_{t_1}^{t_2}dtL$ is written as:
$$\delta I=\int_{t_1}^{t_2}dt\frac{\delta I}{\delta q(t)}\delta q(t)$$
How is ...
1
vote
0answers
316 views
Find equations of motion from given Lagrangian density [closed]
Could someone help me solve this probably not very hard problem?
Given Lagrangian Density:
$\mathcal ...
11
votes
3answers
1k views
7
votes
1answer
176 views
To construct an action from a given two-point function
This is really a basic question whose answer I guess may have to do with the way we construct Feynman rules and diagrams. The question is: Suppose I have been given a two-point function (found in some ...
-1
votes
1answer
143 views
Quantum tunneling in Field theory with Time dependent potential
What should be the limits of integration for euclidean action $S(\phi)$ in 3d and 4d? This action is negatively exponentiated to calculate the decay rate. I suspect that it is variable limit problem.
...
6
votes
2answers
833 views
Why is lagrangian density correct?
The textbooks I have available explain that due to the infinite degrees of freedom of a field, the relevant object in QFT is the lagrangian density. A lagrangian is then obtained for the field by ...
15
votes
3answers
841 views
How general is the Lagrangian quantization approach to field theory?
It is an usual practice that any quantum field theory starts with a suitable Lagrangian density. It has been proved enormously successful. I understand, it automatically ensures valuable symmetries of ...
6
votes
1answer
2k 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.
