All Questions
Tagged with conservation-laws field-theory
85
questions
2
votes
1
answer
48
views
Does Noether's theorem apply to a strict on-shell symmetry of the action that holds on every integration region?
I've worked through different proofs of Noether's theorem and read various posts about it on this site. Some important takeaways, among others from this and this post by Qmechanic were
Every off-...
- 587
1
vote
1
answer
62
views
Symmetry transformation exact meaning
In whatever text/review I happen to come across (like for example From Noether’s Theorem to Bremsstrahlung: A pedagogical introduction to
Large gauge transformations and Classical soft theorems, ...
- 3,992
5
votes
2
answers
643
views
Theorem in mechanics relating energy flow and momentum
In Feynman's Lecture 27 on Vol. II it is written that
There is an important theorem in mechanics which is this: whenever there is a flow of energy in any circumstance at all (field energy or any ...
- 1,831
1
vote
0
answers
51
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Q1.1(a) Sakurai Advanced Quantum Mechanics For energy-momentum tensor [closed]
I need to prove that the energy-momentum tensor density is defined as:
\begin{equation}
\mathcal{T}_{\mu\nu}=-\frac{\partial \phi}{\partial x_\nu}\frac{\partial\mathcal{L}}{\partial(\frac{\partial \...
- 111
2
votes
1
answer
49
views
Derivation of conserved current
Can someone give me some steps on showing the last line.
From the line, $$-\int d^3x \space \epsilon_{abc} \space [ (\nabla^2\phi_b) \phi_c - m^2\phi_b\phi_c ] $$ I cannot actually see how could this ...
- 171
1
vote
0
answers
55
views
What are the conserved quantities in a classical field?
I'm completely new to this. I was trying to derive the conserved current of the following Lagrangian density:
$$
\mathcal L(\phi, \partial_\mu \phi) = \frac{1}{2}\partial_\mu \phi \partial^\mu\phi + \...
- 1,525
0
votes
0
answers
77
views
On the continuity condition of the Klein-Gordon equation
I have to show that $\partial_\mu j^\mu = 0$ for the four-current $j^\mu = \frac{i}{2m}\left(\phi^*\partial^\mu\phi - \phi\:\partial^\mu\phi^*\right)$.
Using the Leibniz rule, one gets to
$$\partial_\...
- 1,644
0
votes
0
answers
36
views
Translation Invariance and Conserved Momentum for scalar fields
In my Quantum Field Theory Notes, the professor said that the Hamiltonian of the scalar field lattice $\sum_{x} w \big[a_x^\dagger a_x +h/2 \big]$ is translation invariant. This implies that there is ...
- 61
1
vote
1
answer
57
views
Conserved Noether current [closed]
I want to prove that in the massless limit $m=0$, Noether's current is conserved:
$$ \partial_{\mu} J^{\mu} = \partial_{\mu} (\psi^{\dagger} \gamma_0 \gamma^{\mu} \gamma_5 \psi ) =0$$
I don't really ...
- 1,124
0
votes
1
answer
204
views
Proof that the axial current is conserved in classical QED
I am trying to use the Lagrangian of QED (without kinetic terms for photons) to prove that the axial current of QED satisfies $\partial_\mu j^\mu_5 = 2im\bar\psi\gamma^5\psi,$ where $j^\mu_5 = \bar\...
- 785
1
vote
1
answer
94
views
Why the classical Euler-Lagrange equation is assumed when deriving the Noether's conserved current?
As known, in QFT, the conserved currents, such as the energy-momentum tensor, can be derived from the Noether's theorem and expressed as the product of the field operators. These conserved currents ...
- 163
1
vote
1
answer
114
views
Conserved current of quartic interaction QFT ($φ⁴$-Theory)
The Lagrangian of the real massless $φ⁴$-theory is
\begin{align}
L=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\lambda\phi^4
\end{align}
Therefore the action integral has the global symmetry
\begin{...
- 505
2
votes
1
answer
174
views
Noether current of a Lagrangian with interactions
I am a bit confused regarding Noether Current. The Lagrangian of two complex scalar fields is
$$
\mathcal{L}=\partial^\mu\phi_i^*\partial_\mu\phi_i-m_i^2|\phi_i|^2+\lambda(\phi_2^3\phi_1+\text{h.c.}).
...
- 129
1
vote
1
answer
121
views
Relativistic invariants of a classical field in 4D fashion: why the relation between the components of the current density holds?
I'm trying to understand how is justified the following relation between the first component of the current density integrated over the volume and the scalar product of the 4-vector current density ...
- 310
0
votes
2
answers
112
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Why Electron Quantum Field Wants Little Energy But Photon Field Doesn't
In this Quora post: https://qr.ae/pv5tac, it states that the electron quantum field "wants" to reduce the energy it has, so when a particle and an anti-particle interact and the charges ...
