The tag has no usage guidance.

learn more… | top users | synonyms

40
votes
1answer
5k views

Differentiating Propagator, Greens function, Correlation function, etc

For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most ...
38
votes
4answers
14k views

Why correlation functions?

While this concept is widely used in physics, it is really puzzling (at least for beginners) that you just have to multiply two functions (or the function by itself) at different values of the ...
7
votes
1answer
1k views

Correlation function which has branch cut in momentum space

When correlation function has branch cut in momentum space, how to find correlation in coordinate space? For example $$ \tilde {G}(\omega) = \frac{2i}{\omega+(\omega^2-\nu^2)^{1/2}}$$ How to get the $...
5
votes
2answers
445 views

Time-ordered operator in Srednicki

On page 51 Srednicki states, "Note that the operators are in time order...we can insert $T$ without changing anything". This I agree with. But then on the next paragraph he states "The time order ...
7
votes
1answer
488 views

Differential equation (Greens function) satisfied by the kernel using path integrals

I'm reading Feynman and Hibbs, Quantum Mechanics and Path Integrals. How do I show that the kernel $$\tag{2-25} K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$$ satisfies the ...
5
votes
2answers
651 views

How do I define time-ordering for Wightman functions?

This is a follow-up question to What are Wightman fields/functions Ok, so based on my reading, the field operators of a theory are understood to be operator-valued distributions, that is, to be ...
4
votes
1answer
263 views

Quantum Field Theory without LSZ, how is it possible?

Most modern texts spend some time deriving the LSZ reduction formula that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you ...
16
votes
1answer
357 views

LSZ reduction vs adiabatic hypothesis in perburbative calculation of interacting fields

As far as I know, there are two ways of constructing the computational rules in perturbative field theory. The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free states,...
5
votes
1answer
923 views

Why do disconnected diagrams not contribute to the S matrix?

I've read somewhere that disconnected diagrams do not contribute to the S-matrix. I don't see why this is the case. I do know why vacuum bubbles do not contribute: given a generating functional for a ...
4
votes
3answers
407 views

Applying theorem of residues to a correlation function where the Fermi function has no poles

Let $n_F(\omega) = \large \frac{1}{e^{\beta (\omega)} + 1}$ be the Fermi function. A fermionic reservoir correlation function is given by: $$C_{12}(t) = \int_{-\infty}^{+\infty} d\omega~ \tag{5}J_R(...
0
votes
1answer
302 views

Applying theorem of residues to a fermionic reservoir correlation function in order to solve the integral in the CF and obtain a summation

Applying theorem of residues to a fermionic reservoir correlation function in order to solve the integral in the correlation function and obtain a summation.
6
votes
1answer
2k views

What are Wightman fields/functions

Simple question: What are Wightman fields? What are Wightman functions? What are their uses? For example can I use them in operator product expansions? How about in scattering theory?
2
votes
1answer
294 views

Green's Functions from Gell-Mann and Low Theorem

What I want to do: $\newcommand{\ket}[1]{\left|#1\right\rangle}$ $\newcommand{\bra}[1]{\left\langle#1\right|}$ $\newcommand{\braket}[1]{\left\langle#1\right\rangle}$ The Gell-Mann Low Theorem tells ...
1
vote
0answers
130 views

Proof of correlation function formula in quantum field theory

I am trying to prove the following formula used in QFT: $$\langle\Omega|T\{\Phi(x_1)\dots\Phi(x_n)\}|\Omega\rangle = \frac{\langle 0|T\{\Phi_I(x_1)\dots\Phi_I(x_n)S\}| 0 \rangle}{\langle 0|S| 0 \...
3
votes
1answer
230 views

Autocorrelation of noise - negative correlation

I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an ...
2
votes
0answers
258 views

Constructing Ward identity associated with conserved currents

Consider constructing the Ward identity associated with Lorentz invariance. It is possible to find a 3rd rank tensor $B^{\rho \mu \nu}$ antisymmetric in the first two indices, then the stress-energy ...
1
vote
1answer
81 views

Physics of detection of coherent light in an incoherent background using the more compact Fabry Perot interfeometer?

I read University Of California Berkeley Professor J. Bokor's Chapter 7 course notes , shown below as an imgur image , on Temporal Coherence tonight. I am sending an email to Professor J. Bokor ...
5
votes
0answers
101 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: $S[\phi,\sigma]=\int{d^4x[-\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2-\frac{1}{2}M^2\sigma^2-\...
0
votes
1answer
45 views

Information that can be extracted from the time-ordered correlation function

The time-ordered correlation function can be very complicated and encodes a tremendous amount of information. For example, the LSZ formula can be used to extract S-matrix elements from the time-...