All Questions
Tagged with semiclassical quantum-field-theory
35 questions
2
votes
0
answers
62
views
How can we calculate simple quantum tunneling processes from the path integral?
I've been reading through Altland and Simons' Condensed Matter Field Theory, and am confused a bit by their discussion on tunneling and instantons. However I don't quite understand how this relates to ...
- 21
4
votes
2
answers
553
views
Making sense of stationary phase method for the path integral
I am trying to understand this paper/set of notes. I have already seen the following related question: Does the stationary phase approximation equal the tree-level term? but had some trouble following ...
- 3,992
4
votes
0
answers
104
views
What do the authors of the paper mean here exactly by path integral?
First of all, please forgive me if i am asking a dumb question. I don't have a physics background. I was reading this paper by Hawking & Hertog on populating string theory landscape and came ...
- 67
1
vote
0
answers
45
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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
1
vote
1
answer
86
views
Semiclassic limit of a QFT in Zinn-Justin
I am reading the Zinn-Justin book "Quantum Field Theory and Critical Phenomena" and i have come across a perplexing point.
Given the partition functional, in Euclidean QFT:
$$Z[J, \hbar] = \...
- 1,853
1
vote
1
answer
101
views
Compatibility of renormalisation with the quantum-classical correspondence principle
We know that Quantum Theories obey the Heisenberg equations of the motion, taking the expected values of which gives us the classical equations.
Also, We replace the mass and coupling parameters of a ...
- 6,666
6
votes
2
answers
558
views
Hawking Radiation without a horizon?
I’m reading this article for a straightforward derivation of the Hawking effect https://www.researchgate.net/publication/...
user310742
4
votes
2
answers
576
views
Conceptual question about Euler-Lagrange equations in Quantum Field Theory
So I've started going down the QFT rabbit hole aided by Schwartz's book "Quantum Field Theory and the Standard Model". On chapter 7, the first method used to find the position-space Feynman ...
- 409
1
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0
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58
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Help to evaluate an integral given in appendix of Quantum Field Theory in a Nutshell [duplicate]
On p. 16 in appendix 3 in section I.2 of Quantum Field Theory in a Nutshell by Zee the integral to be evaluated is $$I = \int_{-\infty}^{+\infty}dqe^{-(1/\hbar)f(q)}.$$
Where $f(q)$ is expanded as
$$...
- 45
7
votes
1
answer
402
views
Does the stationary phase approximation equal the tree-level term?
Consider the scalar field transition amplitude
$$\tag{1} \mathcal{A} = \int_{\phi_i}^{\phi_f} D\phi e^{iS[\phi]/\hbar}. $$
Let $\phi_{cl}$ solve the classical equation $\frac{\delta S}{\delta\phi}=0$. ...
- 1,515
4
votes
3
answers
301
views
Energy conservation in semiclassical gravity
I'd like to know whether semiclassical gravity models contain an energy conservation law with the following (heuristic) form:
$$``\text{Energy of classical spacetime + expected energy of quantum ...
- 1,515
0
votes
1
answer
152
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Response Functions in Field Theory - Subtleties?
The definitions I saw of response functions, e.g. in Landau & Lifschitz (SP Sec. 125), or in Altland & Simons (Ch.7), are given in terms of expectation values of some physical quantity $\...
- 1,657
2
votes
1
answer
101
views
On the computation of functionals in QFT
Using the Gaussian (path)-integral
$$
\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}
$$
my book claims that we can compute the following ...
- 791
3
votes
1
answer
212
views
When can I use Gaussian integration to compute a path integral?
In reading 14.4 of Gregory Moore's notes on abstract group theory, I was left with some questions on the computation he did of the path integral that may be general features.
Let consider a spacetime $...
- 3,985
2
votes
2
answers
176
views
Why the classical configuration always static when applying saddle point (semi-classical) approximation?
For an Green function/partition function:
$$\int D[\phi]e^{\frac{i S[\phi]}{\hbar}}$$
We can make saddle point approximation and gives classical configuration:
$$\delta \mathcal{S}=0\Longrightarrow \...
- 1,652
2
votes
1
answer
153
views
Confusions on expectation value for $\hbar$ going to zero
In Matthew D. Schwartz's QFT book, Chapter 28, the author claims when $\hbar \rightarrow 0$, the following equality (eq 28.4) holds:
So how can I see the second "$=$" holds? It seems the ...
- 1,035
3
votes
2
answers
162
views
Why is there an difference between the exponent of the determinant of these two path integral?
When I read about Altland and Simons “Condensed matter field theory”, I came across with the path integral (3.28).
$$\langle {q_f}|e^{-iHt/\hbar} |q_i\rangle = \det(\frac{i}{2\pi \hbar} \frac{\...
- 503
1
vote
0
answers
373
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Path integrals and classical paths obtained via saddle point integration
EDIT: Focussed my question more based on @octonion's comments
Say one is interested in the following action,
$$S[\{\phi_i(x,t), \tilde{\phi_i(x,t)}\}] = \int \mathrm{d}t\mathrm{d}^d x\left(\tilde{\...
- 151
2
votes
0
answers
164
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WKB solution in QFT: classical action and particle vs antiparticle case
Consider the theory of a complex scalar field
$$S[\psi, \psi^\dagger] = -\int d^4x \left(\hbar \partial_\mu \psi^\dagger \partial^\mu\psi + \hbar^{-1} m^2 |\psi|^2\right)$$
giving the Klein-Gordon ...
- 781
1
vote
1
answer
423
views
Why are Grassmann variables the classical limit of fermions?
In many texts the anti-commutation relations for fermions are given as
$$\{ \bar{\psi}^\alpha (\vec{x}), \psi^\beta(\vec{y}) \} = \delta^{\alpha\beta} \delta(\vec{x} - \vec{y})$$
$$\{ \psi^\alpha (\...
- 161
6
votes
1
answer
814
views
Difference between QFT In curved spacetime, semiclassical, and quantum gravity?
Could someone describe the difference, qualitatively, between QFT in curved spacetime, semiclassical gravity, and quantum gravity? I know that each is an approximation to the next and the end goal is ...
user203234
4
votes
2
answers
299
views
Quantum corrections in path integral
I am working the following exercise:
Calculate the generating functional $$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),$$ $...
- 1,237
3
votes
2
answers
298
views
Stability of the Hawking-Hartle vacuum in semiclassical gravity
Consider a free quantum field theory defined upon a static Lorentzian spacetime possessing a bifurcate Killing horizon, such as Schwarzschild spacetime.
These assumptions are sufficient to define a ...
- 4,321
2
votes
0
answers
88
views
Why is the semiclassical approximation of the abelian Chern-Simons theory exact?
I was told that in abelian Chern-Simons theory (say, with a general level matrix $K$), semiclassical approximation is exact because there is no trivalent vertex, which in non-abelian case makes the ...
- 432
2
votes
1
answer
155
views
How I can see that everyday life systems behave classical (from QFT path integrals)?
If I would try to treat macroscopic systems consisting of a super-large number of particles (also when environment is included), I have to compute $2N$-point correlation functions with very large ...
- 3,518
2
votes
1
answer
122
views
Time zero fields using operator valued distributions on QFT on curved spacetimes
On Fewster's notes on QFT on curved spacetimes he says:
Our goal is to find operators $\Phi(f)$ such that
$$\Phi(Pf) = 0$$
for all $f\in C^\infty_0(M)$ and so that the time zero fields
$$\varphi({\bf{...
- 37.4k
1
vote
1
answer
146
views
Quantum Anomalies: Is there a way to show that we recover a classical symmetry that does not exist quantum mechanical in the classical limit?
Quantum Anomalies: Is there a way to show that we recover a classical symmetry that does not exist quantum mechanical in the classical limit?
From undergraduate quantum mechanics, I know that we ...
- 7,860
3
votes
1
answer
231
views
In the semiclassical approximation, should I expand the generating functional around saddles of the sourced or the unsourced action?
Consider a Euclidean path integral say in a real scalar field theory.
$$
\int d[\phi]\exp(-I[\phi])
$$
In the semiclassical approximation, we consider stationary points of the action and expand ...
- 6,137
6
votes
1
answer
189
views
Why do we have to sum the expansions around all the action's stationary points?
This is in some sense a follow-up question to my previous question Why is it OK to keep the quadratic term in the small $\hbar$ approximation?. I understand how we can expand the action around a ...
- 6,137
2
votes
2
answers
443
views
Generalisation of a particle in QFT
In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
- 6,980
2
votes
2
answers
380
views
Semiclassical approximation in Quantum Field Theory
I've recently stumbled upon a semiclassical approximation to quantum field theory that I've never heard of and have a hard time understanding. Consider the Hamiltonian,
\begin{equation}
H = \frac{c}{ ...
- 9,005
12
votes
1
answer
2k
views
Eikonal approximation in QFT
Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
- 5,192
1
vote
1
answer
883
views
Semiclassical Approximation
In many books I read about semiclassical approximation applied to the field of Bose-Einstein condensation.
But I don't understand what it really means.
For example I read that an expression like this
...
- 417
15
votes
1
answer
1k
views
Hawking Radiation as Tunneling
Firstly, I'm aware that Hawking radiation can be derived in the "normal" way using the Bogoliubov transformation. However, I was intrigued by the heuristic explanation in terms of tunneling. The ...
- 17k
58
votes
6
answers
12k
views
Tree-level QFT and classical fields/particles
It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree-level cross-section for electron-electron scattering ...
Squark