The path-integral tag has no wiki summary.
26
votes
5answers
1k views
Path integral vs. measure on infinite dimensional space
Coming from a mathematical background, I'm trying to get a handle on the path integral formulation of quantum mechanics.
According to Feynman, if you want to figure out the probability amplitude for ...
9
votes
5answers
1k views
Why not using Lagrangian, instead of Hamiltonian, in non relativistic QM?
When we studied classical mechanics on the undergraduate level, on the level of Taylor, we covered Hamiltonian as well as Lagrangian mechanics.
Now when we studied QM, on the level of Griffiths, we ...
3
votes
1answer
245 views
More on the Feynman Path Integral Formula in Brian Cox' Lecture and its Consequences
This is a continuation of this question about Brian Cox' lecture Night with the Stars.
I know the main steps to get from $K(q",q',T)=\sum_{paths}Ae^{iS(q",q',T)/h}$ to $\Delta t ...
1
vote
1answer
1k views
Feynman Path Integral Formula in Brian Cox' “A Night with the Stars” Lecture
The Youtube link keeps breaking, so here is a search on Youtube for Brian Cox' A Night with the Stars lecture. Pause the video on 40.32minutes.
What you see he said is called Feynman's Path Integral.
...
7
votes
3answers
852 views
Once a quantum partition function is in path integral form, does it contain any operators?
Once a quantum partition function is in path integral form, does it contain any operators?
I.e. The quantum partition function is $Z=tr(e^{-\beta H})$ where H is an operator, the Hamiltonian of the ...
5
votes
5answers
345 views
What is the path integral exactly?
I asked a question here about path integrals and QFT. I just want to confirm something. Is the path integral in quantum field theory a mathematical tool only? I thought the path integral meant that ...
1
vote
1answer
283 views
Why path integral approach may suffer from operator ordering problem?
In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path.
What did ...
7
votes
4answers
380 views
How can there be a quantum field theory that predicts all particle masses?
Say I have a theory with only one (energy) scale, e.g. one given by the fundamental constants
$$\epsilon=\sqrt{\dfrac{\hbar c^5}{G}}.$$
In this case, where I can't compare to something else, is ...
8
votes
5answers
503 views
Why is the contribution of a path in Feynmans path integral formalism $\sim e^{(i/\hbar)S[x(t)]}$
In Feynmans book "Quantum Mechanics and Path Integrals" Feynman states that
the probability $P(b,a)$ to go from point $x_a$ at time $t_a$ to the point $x_b$ at the time $t_b$ is $P(b,a) = ...
5
votes
4answers
252 views
Physical Interpretation of the Integrand of the Feynman Path Integral
In quantum mechanics, we think of the Feynman Path Integral
$\int{D[x] e^{\frac{i}{\hbar}S}}$ (where $S$ is the classical action)
as a probability amplitude (propagator) for getting from $x_1$ to ...
2
votes
1answer
239 views
Classical limit of the path integral formulation of quantum mechanics
It is well-known that if $S \gg \hbar$, then the classical path dominates the Feynman path integral. But is there some to show that if $S\gg\hbar$, then the particle's trajectory will approach the ...
6
votes
2answers
307 views
Lagrangians combining terms with 1 and 2 derivatives
How are field theory Langrangians treated when some terms have 2 derivatives but others have only 1? Because the number of derivatives in a Lagrangian term is more easily even than odd, the ...
6
votes
2answers
718 views
Wheeler-Feynman theory, QED without fields, vacuum polarization
Initially Wheeler and Feynman postulated that, the electromagnetic field is just a set of bookkeeping variables required in a Hamiltonian description. This is very neat because makes the point of ...
3
votes
3answers
287 views
Quantum field theory, particle interpretations and path integrals?
I am trying to find some names or models of a particle interpretation of quantum field theory which isn't a literal path integral approach? Are there any particle interpretations of quantum field ...
1
vote
1answer
134 views
Path Integrals Page Peskin
Hi this problem relates directly to path integrals but I imagine it is a maths trick that I am missing. One has an expression such as $$\int dx \exp\left[i\frac{(p)^{2}}{2}-iV(\frac{f}{4})\right] $$ ...
