Bethe-Salpeter equation confused

[Neitrino]

Dear PF,

Im reading something about bound states & there I one question.
The Bethe-Salpeter equation for a bound pair B deals with the amplitude:

Phi (x,y)=<0|TPsi(x)Psi_bar(y)|B>, |B> is a bound pair state, <0| vacuum...what i missunderstand how it can be the transition between some bound state and vacuum? What about conseravation rules..
Or generally what amplitude is it what transition does it describe?

If I even wright something bad pls correct me.
Thks

Any books where this is described?

 

[azntoon]

The Bethe-Salpeter equation for a bound pair B describes the amplitude of a transition between a bound state and the vacuum. Conservation rules, such as energy and momentum conservation, still apply. The amplitude Phi (x,y) is related to the probability amplitude of the transition occurring. This equation is often used to describe the interactions between particles in atomic and molecular systems. You can find more information about the Bethe-Salpeter equation in books such as "Quantum Mechanics: A Textbook for Undergraduates" by Oleg V. Prezhdo and "Many-Body Quantum Theory in Condensed Matter Physics" by Henrik Bruus and Karsten Flensberg.

 

[denian]

The Bethe-Salpeter equation is a mathematical equation used to describe the behavior of bound states in quantum field theory. It is often used in the study of nuclear and particle physics. It may seem confusing at first, but with some background knowledge in quantum mechanics and field theory, it can be better understood.

The equation deals with the amplitude, or probability, of a bound state B to exist at two different points in space, x and y. This amplitude is denoted as Phi(x,y) and is calculated using the creation and annihilation operators for the bound state, Psi(x) and Psi_bar(y). The <0| represents the vacuum state, which is the lowest energy state in the system.

The transition mentioned is the transition between the bound state B and the vacuum state. In other words, the equation is describing the probability of the bound state to exist in a specific location, while taking into account the effect of the vacuum state.

Conservation rules, such as energy and momentum conservation, are still valid in the Bethe-Salpeter equation. The equation incorporates these rules in its calculations.

In general, the amplitude described in the Bethe-Salpeter equation represents the probability of the bound state to exist at two different points in space. This is important in understanding the behavior of bound states in quantum field theory.

There are many books and resources available that explain the Bethe-Salpeter equation in more detail. Some recommended books include "Quantum Field Theory" by Lewis Ryder and "An Introduction to Quantum Field Theory" by Michael Peskin and Daniel Schroeder. You can also find online resources and lectures that explain the equation in a more accessible way. Keep studying and asking questions, and you will gain a better understanding of this important equation.