All Questions
Tagged with lagrangian-formalism semiclassical
11 questions
0
votes
0
answers
28
views
In which cases does the action obey $\frac{\partial S}{\partial t}=-E$? [duplicate]
I'm reading https://web.physics.utah.edu/~starykh/phys7640/Lectures/FeynmansDerivation.pdf and the article states that there are cases where the action obeys $\frac{\partial S}{\partial t}=-E$. Is ...
- 1
1
vote
0
answers
45
views
Mesons as a two-body problem is semiclassical QCD?
In particle physics and quantum field theory, mesons are interpreted as a system composed of a quark and an anti-quark, and the color charge of both must be at each opposite moment (green/anti-green, ...
- 1,670
2
votes
1
answer
376
views
How to use saddle point approximation with path integrals?
i would like to evaluate $$\int\mathcal{D}x\ e^{-\int\limits_{-\infty}^{\infty} dt\ (\dot x+\alpha x)^2}\tag{1}$$
and it is my understanding that the way to do so is using the saddle point ...
- 31
3
votes
0
answers
107
views
Meaning of equations associated with Legendre transform
In the famous paper about semiclassical Bloch theory https://arxiv.org/abs/cond-mat/9511014, the Lagrangian
\begin{eqnarray}
L (\mathbf{k},\dot{\mathbf{k}}) = -e \delta \mathbf{A}(r,t)\cdot\dot{\...
2
votes
0
answers
92
views
Semi-classical limit of Feynman path integral
I am reading Blau's note on The Path Integral Approach to Quantum Mechanics. I am troubled for the derivations of semi-classical limit of Feynman path integral, which is located on Page.50 of Blau's ...
- 1,473
0
votes
1
answer
273
views
How Feynman's path integral lead to least action principle? Math proof needed [duplicate]
I have read about Feynman path integral which leads to classical limit.
It said that because $\hbar \rightarrow 0$ in classical view. The function of path integral $\int e^{\frac{1}{\hbar}f(x)} dx$ ...
2
votes
1
answer
101
views
On the computation of functionals in QFT
Using the Gaussian (path)-integral
$$
\int \mathcal{D}\eta e^{i\int_{t_i}^{t_f} dt \eta(t) O(t) \eta(t)} = N [\operatorname{det} O(t)]^{-1/2}
$$
my book claims that we can compute the following ...
- 791
1
vote
1
answer
180
views
Stationary Phase approximation with multiple coordinates?
The stationary phase approximation can be used to find an approximate value for the path integral
\begin{equation}\int Dx e^{-S[x]} \approx e^{-S[\bar{x}]} \left(\det{\frac{\hat{A}}{2 \pi}}\right)^{-1/...
4
votes
2
answers
299
views
Quantum corrections in path integral
I am working the following exercise:
Calculate the generating functional $$Z[j]=\int \mathcal{D}\Phi \exp\left(\frac{i}{\hbar}S[\Phi,j]\right),\quad S[\Phi,j]=\int d^4x(\mathcal{L}(\Phi)+j\Phi),$$ $...
- 1,237
2
votes
1
answer
532
views
Classical spin viewed as $SU(2)$
In which sense is the configuration variable of a classical spin $SU(2)$? I can view a classical spin as a unit vector in $\mathbb{S}^2$ (2-dim. sphere), but it seems it is really given by a matrix $U$...
- 121
19
votes
2
answers
5k
views
Semiclassical limit of Quantum Mechanics
I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into ...
- 4,169