# What is the physical meaning of Bogoliubov transformation?

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## Main Question or Discussion Point

hi guys
i recently was reading about hawking radiation and how he overcome the lack of a theory for quantum gravity by using a mathematical trick ( to see the effect of gravity on quantum fields ) and this trick was the Bogoliubov transformation .... , i just want some one to briefly explain what is the physical meaning of it and how its being applied ( i am not very familiar with creation and annihilation operators in quantum mechanics ... i tried to search online but it was somehow complicated to understand ) , could some one explain it to me with a simpler analogy ?

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atyy
The use of the Bogoliubov transform in Hawking radiation is not really related to overcoming the lack of a theory of quantum gravity. Hawking was using well accepted principles, but whose consequences were not well understood.

A simple analogy for why the Bogoliubov transformation is useful is given by the Fourier transform or the Laplace transform. When a linear differential equation is Fourier or Laplace transformed, we can change the problem to an equivalent problem in simple algebra, which can be easily solved.

A. Neumaier
2019 Award
A simple analogy for why the Bogoliubov transformation is useful is given by the Fourier transform or the Laplace transform. When a linear differential equation is Fourier or Laplace transformed, we can change the problem to an equivalent problem in simple algebra, which can be easily solved.
But Bogoliubov transformations change the nature of the problem in the thermodynamic limit, and produce in many important cases (e.g., superconductivity; see, e.g., https://en.wikipedia.org/wiki/Cooper_pair) phase transitions.

A good introduction to creation and annihilation operators for statistical mechanics is in the book by Linda Reichl.

Demystifier
A good introduction to creation and annihilation operators for statistical mechanics is in the book by Linda Reichl.
The author as written in the book is L.E. Reichl. I didn't know that Reichl is a woman. EDIT: I've just realized that I had the old 2nd edition, and that now there is a significantly different 4th edition.

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Demystifier
i am not very familiar with creation and annihilation operators in quantum mechanics
Without that, I'm afraid, you cannot understand particle creation described by Bogoliubov transformation.

A. Neumaier
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