The path-integral tag has no wiki summary.
14
votes
4answers
234 views
Is every quantum measurement reducible to measurements of position and time?
I am currently studying Path Integrals and was unable to resolve the following problem. In the famous book Quantum Mechanics and Path Integrals, written by Feynman and Hibbs, it says (at the beginning ...
1
vote
2answers
157 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?
2
votes
1answer
29 views
Diagonalizing/eigenvalues of the infinite dimensional matrix of N harmonic oscillators on a ring
I have trying to show that the continuum limit of N quantum harmonic oscillators gives rise the the klein-gordon field. However, instead of a usual finite string, I want to do it on a ring. Hence, my ...
5
votes
0answers
205 views
Gaussian Integrals : Functional determinant expressed as a trace
Be $A_{ij}$ a symmetric matrix. Then I can easily write
$$
\int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx=
\sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log ...
4
votes
0answers
187 views
When can the source term of a partition function be put in?
More specifically, in quantum field theory books, we usually have this:
\begin{equation}
Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_l [\bar{\eta}_l (\tau) \psi_l (\tau) + ...
3
votes
0answers
124 views
Inclusion of information about external particles to calculate scattering amplitudes
In this (schematic) equation to calculate the scattering amplitude A by integrating over all possible world sheets and lifetimes of the bound states
$$ A = \int\limits_{\rm{life time}} d\tau ...
2
votes
0answers
132 views
What is the relationship between consistent histories and path integrals?
As can for example be learned from chapter I.2 of Anthony Zee's Quantum field theory in a nutshell, path integrals can be used to to calculate the amplitude for a system to transition from one state ...
1
vote
0answers
74 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 ...
1
vote
0answers
62 views
Chemical reaction as state transition?
When considering diffusion of chemicals, the reaction part is business of chemical kinetics, where the relevant characteristics of different substances come from collision theory together with some ...
0
votes
0answers
54 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 . ...
