Linked Questions

40 votes
6 answers

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 ...
user avatar
26 votes
3 answers

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 ...
JamesMarshallX's user avatar
25 votes
3 answers

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 ...
user avatar
19 votes
3 answers

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 ...
Turion's user avatar
  • 669
22 votes
2 answers

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 ...
toot's user avatar
  • 2,866
7 votes
2 answers

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 ...
Javier's user avatar
  • 27.6k
1 vote
2 answers

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 ...
user183966's user avatar
7 votes
2 answers

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{\...
knzhou's user avatar
  • 99.8k
1 vote
1 answer

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 ...
Kvothe's user avatar
  • 779
6 votes
1 answer

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 ...
123hoedjevan's user avatar
2 votes
0 answers

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 ...
Phil Tosteson's user avatar
0 votes
0 answers

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 ...
mathquest's user avatar
  • 166