The path-integral tag has no wiki summary.
1
vote
1answer
90 views
Discretization of action in path integral
I am reading Peskin and Schroeder (path integrals) and it states that discretising the classical action gives:
$$S~=~\int \left(\frac{m}{2}\dot{x}^{2}-V(x)\right)
dt ~\rightarrow~ \sum ...
0
votes
1answer
91 views
Path Integrals Page 278-9 Peskin
Hi this problem relates directly to path integrals on pages 278 to 279 but I imagine it is a maths trick that I am missing. One has an expression such as $$\int dx ...
5
votes
4answers
190 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 ...
1
vote
1answer
50 views
Path integral with boundary and bulk terms
I was wondering if their is a general strategy for computing path integrals with a mix of boundary and bulk integral actions. Do people use divergence theorem to convert the action into bulk ...
5
votes
5answers
319 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 ...
3
votes
3answers
262 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 ...
6
votes
3answers
304 views
When does $\hbar \rightarrow 0$ provide a valid transition from quantum to classcial mechanics? When and why does it fail?
Lets look at the transition amplitude $U(x_{b},x_{a})$ for a free particle between two points $x_{a}$ and $x_{b}$ in the Feynman path integral formulation
$U(x_{b},x_{a}) = \int_{x_{a}}^{x_{b}} ...
1
vote
1answer
261 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 ...
1
vote
1answer
115 views
How would Lagrangian be used tor recover Schrodinger equation?
In path integral formulation of quantum mechanics, I heard that Lagrangian is defined. So, how would Lagrangian in this formulation be used to recover Schrodinger equation that we normally use?
1
vote
1answer
99 views
Is the following a simpler viable alternative to Feynman's interpretation of the double slit experiment
Feynman suggested that there is an infinity of trajectories for a single electron travelling from the source to the phosphorescent screen. He said that one electron goes through both holes (Fig 4.10, ...
1
vote
0answers
65 views
Solving the path integral for $(ax)^4-(bx)^2$ potential
I need help in solving the path integral of potential given by the form
$(ax)^4-(bx)^2$
This potential is maybe known as Ginzberg Landau potential
I tried using the approximation in which the ...
0
votes
0answers
53 views
path integrals: how/why can the phase be identified with the action?
In Peskin & Schroeder, chapter 9 introduces the functional methods.
The idea, to recall, is simply to sum over all the possible paths:
$U(x_a,x_b;T) = \sum_{\text{all paths}} e^{i . ...
4
votes
4answers
369 views
What's the role of classically forbidden paths in path integral?
I'm interested in how and how much classically-forbidden paths contribute to a path integral? Is there any good reference on the issue? Any discussion in QM or QFT context would be appreciated.
...
12
votes
1answer
200 views
Can path integrals be used to understand entanglement?
I like path integrals. I prefer to try to understand quantum phenomena in terms of path integrals rather than Hamiltonian mechanics. However, most of the standard texts on quantum mechanics start from ...
6
votes
1answer
161 views
Change of variables in path integrals
I need to evaluate a path integral which involves a set of fields $X=\left\{ \psi_i \right\}$:
$$ I = \int \prod_i \mathcal{D} \psi_i e^{-S \left[ \left\{ \psi_i \right\} \right] } $$
In order to ...
