Simple question from Peskin Schroeder

In summary, the conversation discusses the expression <0|\phi(x)\phi(y)|0> and how it relates to the creation of one-particle states at positions x and y. There is also a question about the formula <0|\phi(x)|p>=...e^ipx and its relationship to the projection of a single-particle state onto the <x| basis. It is clarified that <0|\phi(x)=<x| is a simple calculation and has no special physical significance.
  • #1
Neitrino
137
0
Gentlemen,
Could you help me please, I am sure it is not even worthy of your attention, but anyway...

In Peskin, Schroeder - from expresion [tex] <0|\phi(x)\phi(y)|0> [/tex] survives [tex] <0|a_p a_q^\dag|0> [/tex] so it creates one-particle state |q> at position y and another one-particle state | p> at postion x. But how do I intuitively see that causuality/propagation of particle between these positions is imbeded and considered in that expresion?

And another question [tex] <0|\phi(x)|p>=...e^ipx[/tex] formula 2.42

it's said that it is a position-space representation of the state |p> just as in NR QM <x|p>, so it should be projection of single-particle |p> state onto the <x| baisis and what vectors/basis that state is projected on? where is that <x| vectors in 2.42

P.S. I am sure i missed something very simple in understanding of above and that's why posting such "silly" questions

Thanks in advance
 
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  • #2
(1) I think the expresion [tex] <0|\phi(x)\phi(y)|0> [/tex]
survives [tex] <0|a_p a_q^\dag|0> [/tex] means:
[tex] <0|a_p^\dag a_q^\dag|0> [/tex]=0 and [tex] <0|a_p a_q|0> [/tex]=0;
only [tex] <0|a_p a_q^\dag|0> [/tex] survives, of course p and q are arbitary,
not single p and single q. the final result will be an integral over all possible p or q.

(2) [tex] <0|\phi(x)=<x|[/tex], this is a simple calculation.
there is no special physical significance here, the author, I guess, just mentioned NR
case to make the formula be easily understood.
 
  • #3
snooper007 said:
(2) [tex] <0|\phi(x)=<x|[/tex], this is a simple calculation.

Dear Snooper007 thks for ur reply..
but [tex] <0|\phi(x)[/tex] it is a complex conjugation of [tex] \phi(x)|0>[/tex] (as u mentioned in QM forum). So [tex] <0|\phi(x)=\int{\frac{d^3 p}{(2\pi)^3}\frac{1}{2E_p}e^{ipx}<p|[/tex]

but with [tex] <0|\phi(x)=<x|[/tex] I am confused <-How/why it's that?
 

1. What is "Simple question from Peskin Schroeder"?

"Simple question from Peskin Schroeder" is a commonly used phrase in the field of quantum field theory, named after the authors of the textbook "An Introduction to Quantum Field Theory" by Michael Peskin and Daniel Schroeder. It refers to a specific type of question that is often asked in introductory courses or discussions about quantum field theory.

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A "Simple question from Peskin Schroeder" is typically a basic question about the fundamental concepts and principles of quantum field theory, such as the meaning of certain equations or the interpretation of physical phenomena. These questions are often used to test understanding and engage in deeper discussions about the subject.

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Some examples of "Simple question from Peskin Schroeder" include asking about the meaning of the Klein-Gordon equation, the difference between bosons and fermions, or the concept of gauge symmetry. These are all fundamental concepts in quantum field theory that are often discussed and explained in introductory courses.

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