What is the propagation amplitude of a particle in QFT?

[Sombrero]

Hola everybody, this is my first visit to PF.
Can anyone help me please...my question is from QFT textbook
phi(x)|0> is creation of particle at position x, being in superposition of momenum states - - - - correct?
<0|phi(y) is birth of particle at position y. So if I consider both expressions i have two particles one born at position x, another particle born at position y.

Phi (x) Phi (y) already in Heisenberg picture.

Why <0|phi(y)phi(x)|0> why is this the propagation amplitude of particle from x to y as said in Peskis and Schroeders book? I have just two particles at x and y, One particle has been created at x, another at position y.

Gracias

 

[vanesch]

Hello Sombrero and welcome to PF !

Have already a look at the following thread where a very similar question was raised:

https://www.physicsforums.com/showthread.php?p=761339#post761339

and don't hesitate to ask or discuss here.

cheers,
Patrick.

 

[denian]

for your question. In quantum field theory (QFT), particles are described as excitations of a quantum field. The field is a mathematical entity that pervades all of space and time, and the particles are created and destroyed by the field. The propagation amplitude of a particle in QFT represents the probability amplitude for a particle to travel from one point in space to another.

In the expression <0|phi(y)phi(x)|0>, the first phi(x) creates a particle at position x and the second phi(y) annihilates a particle at position y. This expression represents the amplitude for a particle to be created at x and then travel to y, or for a particle to be annihilated at y and then travel to x. This is why it is considered the propagation amplitude of a particle from x to y.

In QFT, particles are described as excitations of the field, rather than individual particles with definite positions and momenta. This is because of the uncertainty principle, which states that the more precisely we know a particle's position, the less precisely we know its momentum, and vice versa. So, in QFT, particles can exist in a superposition of momentum states, as you correctly stated.

I hope this helps to clarify the concept of propagation amplitude in QFT. It is a fundamental concept in understanding the behavior of particles in this theory. If you have any further questions, please don't hesitate to ask. Best of luck with your studies!