Tagged Questions
2
votes
1answer
88 views
Path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $
How do I calculate path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $ where $t_i<t_1<t_f$? I am doing this by discretizing, the time intervals and adding a complete set of ...
1
vote
2answers
136 views
Path Integral Quantization
I was reading through my notes on the path integral quantization of bosonic string theory when a general question about path integral quantization arised to me.
The widely used intuitive explanation ...
5
votes
2answers
75 views
Calculating the the kernel using path integrals for quadratic lagrangians
I am reading Feynman and Hibbs on Path Integrals. In section 3.5, they show that the kernel for a lagrangian of the form $L=a(t)\dot{x}^2+b(t)\dot{x}x+c(t)x^2+d(t)\dot{x}+e(t)x+f(t)$ is ...
1
vote
2answers
118 views
$\langle B|A \rangle$ expressed in terms of the Partition Function
Say you have an electron departing from point A and reaching poing B after a time t.
According to some helping friend, the Partition Function for that electron going from point A to B can be written ...
5
votes
4answers
277 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 ...
6
votes
5answers
389 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
298 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
300 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 ...
4
votes
4answers
387 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
224 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
197 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 ...
2
votes
2answers
247 views
Intuition for Path Integrals and How to Evaluate Them
I'm just starting to come across path integrals in quantum field theory, and want to get the right intuition for the them from the start. The amplitude for propagation from $x_a$ to $x_b$ is typically ...
3
votes
1answer
139 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
$$ A = \int\limits_{\rm{life time}} d\tau ...
6
votes
1answer
239 views
What is the value of a quantum field?
As far as I'm aware (please correct me if I'm wrong) quantum fields are simply operators, constructed from a linear combination of creation and annihilation operators, which are defined at every point ...
5
votes
1answer
212 views
Path integral with zero energy modes
Consider the field integral for the partition function of a free non-relativistic electron in a condensed matter setting, i.e.
$$ Z = ∫D\bar\psi D\psi \exp\left(-\sum_{k,ω} \bar\psi_{k,ω} (-iω + ...
5
votes
0answers
214 views
Gaussian Integrals : Functional determinant expressed as a trace
Be $A_{ij}$ a symmetric matrix. Then I can easily write
$$
\int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx=
\sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log ...
4
votes
2answers
319 views
Path integral and geometric quantization
I was wondering how one obtains geometric quantization from a path integral. It's often assumed that something like this is possible, for example, when working with Chern-Simons theory, but rarely ...
1
vote
1answer
166 views
Importance of phase in probability amplitude in QFT
I have started teaching myself QFT from the textbook by A. Zee. From reading that book, my idea of a path integral in field theory is the probability amplitude to go from a given field configuration ...
4
votes
1answer
137 views
Calculating equation of motion using path integral
Suppose my action integral is $S=\int d^4x(\nabla \times A)^2$ and $\delta S$ gives $\delta S =\int d^4x [2(\nabla \times A).(\nabla \times \delta A)]$
I would like to calculate the coefficient of ...
6
votes
2answers
195 views
Surface terms for field path integrals?
My question relates to something that I´ve seen in many books and appears in all its glory here: Ryder, pg 198
My question is about eq. 6.74. Which I repeat below:
$$i \int {\cal D}\phi \frac{\delta ...
4
votes
1answer
223 views
Does the vacuum energy problem of quantum field theory only occur in the Hamiltonian approach, or also in the path integral approach and in AQFT?
In a standard QFT class, you're being indoctrinated that there is the "infinite vacuum energy density problem".
(This is sometimes paraphrased as the "cosmological constant problem", which is in my ...
7
votes
4answers
386 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 ...
3
votes
2answers
321 views
Discrete version of Feynman path integrals
I've decided to put a very limited amount of my time into understanding the path integral formulation of quantum mechanics. I'm interested in the mathematical formalism more than the physics, so I'd ...
5
votes
1answer
174 views
Integrating over a gauge field in the field integral formalism
I'm currently trying to study a chapter in Altland & Simons, "Condensed Matter Field Theory" (2nd edition) and I'm stuck at the end of section 9.5.2, page 579.
Given the euclidean Chern-Simons ...
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 ...
1
vote
1answer
181 views
Does path integral and loop integral in a Feynman diagram violate special relativity?
Consider a correlation function between two points A(x1,t1) and B(x2,t2), we need to integrate over paths which could be ...
4
votes
1answer
329 views
Vacuum Wavefunctional
I am having this problem in understanding the vacuum wavefunctional in QFT. Hence this naive question.
I mean, if someone say vacuum wavefunctional, I can think of an element like wavefunction as in ...
9
votes
3answers
204 views
On-shell symmetry from a path integral point of view
Normally supersymmetric quantum field theories have Lagrangians which are supersymmetric only on-shell, i.e. with the field equations imposed. In many cases this can be solved by introducing auxilary ...
8
votes
2answers
143 views
Are there rigorous constructions of the path integral for lattice QFT on an infinite lattice?
Lattice QFT on a finite lattice* is a completely well defined mathematical object. This is because the path integral is an ordinary finite-dimensional integral. However, if the lattice is infinite, ...
2
votes
2answers
1k views
When can I use Wick's theorem?
Wick's theorem means that for fermions, a four point correlation function (for example) can be written in terms of two point correlation functions:
\begin{equation}
\langle b_l^\dagger b_l ...
13
votes
2answers
71 views
Calculating correlation functions of exponentials of fields
In their book Condensed Matter Field Theory, Altland and Simons often use the following formula for calculating thermal expectation values of exponentials of a real field $\theta$:
$$ \langle ...
13
votes
2answers
175 views
Applications of the Feynman-Vernon Influence Functional
I am looking for a reference where the Feynman-Vernon influence functional was defined and used in the context of relativistic quantum field theory. This functional is one method to describe ...
14
votes
1answer
63 views
Instantons and Non Perturbative Amplitudes in Gravity
In perturbative QFT in flat spacetime the perturbation expansion typically does not converge, and estimates of the large order behaviour of perturbative amplitudes reveals ambiguity of the ...
3
votes
2answers
339 views
When is many-body perturbation theory valid?
I'm calculating expectation values (thermal, time-independent) using many-body perturbation theory, but I'm unsure how to work out what values the parameter I'm expanding the perturbation series in ...
6
votes
2answers
314 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 ...
8
votes
1answer
487 views
Questions about the Dyson equation
I'm studying finite temperature many-body perturbation theory, and am trying to understand The Dyson equation. In particular, I'm using Mattuck - A guide to Feynman diagrams in the many body problem.
...
4
votes
0answers
190 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) + ...
6
votes
2answers
729 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 ...
