Linked Questions
12 questions linked to/from How to derive the theory of quantum mechanics from quantum field theory?
41
votes
6
answers
4k
views
Is there a theorem that says that QFT reduces to QM in a suitable limit? A theorem similar to Ehrenfest's theorem?
Is there a theorem that says that QFT reduces to QM in a suitable limit?
Of course, it should be, as QFT is relativisitc quantum mechanics.
But, is there a more manifest one? such as Ehrenfest's ...
Youngsub
26
votes
3
answers
3k
views
Quantum field theory variants
Wikipedia describes many variants of quantum field theory:
conformal quantum field theory
topological quantum field theory
axiomatic/constructive quantum field theory
algebraic quantum field theory
...
- 553
28
votes
3
answers
8k
views
In what sense is a quantum field an infinite set of harmonic oscillators?
In what sense is a quantum field an infinite set of harmonic oscillators, one at each space-time point?
When is it useful to think of a quantum field this way?
The book I'm reading now, QFT by ...
user41404
19
votes
3
answers
4k
views
Are Classical Field Theory and Quantum Mechanics of a single particle (nonrelativistic or "classical") limits of Quantum Field Theory?
Recently I talked about QFT with another physicist and mentioned that the Quantum Field Theory of a fermion is a quantisation of its one-particle quantum mechanical theory. He denied this and ...
- 679
23
votes
2
answers
8k
views
Schrödinger equation from Klein-Gordon equation?
One can view QM as a 1+0 dimensional QFT, fields are only depending on time and so are only called operators, and I know a way to derive Schrödinger's equation from Klein-Gordon's one.
Assuming a ...
- 2,926
8
votes
2
answers
1k
views
Making precise the statement "particles are excitations in a quantum field"
I've been trying to self teach QFT lately. I find that the basic physical idea makes sense, and I can keep up with the mathematical formalism without too much trouble, but I'm having trouble ...
- 28.4k
7
votes
2
answers
742
views
Transferring between field and single-particle versions of the Dirac equation
Schwartz's quantum field theory text moves between spinor fields and individual particles slickly, and I'm wondering what the justification is. To review, the Lagrangian
$$\mathcal{L} = \overline{\...
- 104k
1
vote
2
answers
1k
views
What is the precise formal correspondance between an oscillator and a quantum field?
A common route of introduction to quantum field theory is to note a similarity between the mathematical structure of a quantum harmonic oscillator and of a quantum field "at a point". The quantised ...
- 469
1
vote
1
answer
890
views
Retrieving full Schrodinger equation (including potential) from QFT
I believe that all of Quantum Mechanics should be retrievable from QFT (in 3+1 dimensions) by taking some appropriate limits and/or integrating out degrees of freedom.
David Tong shows in his ...
- 871
6
votes
1
answer
426
views
SHO in QM and Klein Gordon field in 1+0D QFT
The SHO in QM with mass $m=1$ has action
$$
S[x] = \int dt \frac{1}{2} \dot x^2 + \frac{1}{2}\omega^2 x^2
$$
by integration by parts we see this is the same as 1 dim Klein Gordon QFT action with ...
- 332
0
votes
0
answers
243
views
Waves in quantum field theory
There are two sources of 'waviness" in quantum field theory: waves in the underlying classical field, and the Schrodinger equation. I'm learning QFT using the notes by David Tong (I believe they ...
- 162
2
votes
0
answers
191
views
Two ways of thinking about the Dirac equation
My impression is that there are two ways of thinking about the Dirac equation:
Quantum Mechanically: Here we think of the spinor $\phi$ as a generalization of the Schrodinger wave function which ...
- 166