# Why QFT in condensed matter physics?

#### IRobot

I am currently following a course of condensed matter physics and quite enjoying it. But after doig some research I found that many book deal with QFT applied to condensed matter. I wonder what all the calculus of QFT is needed to describe those phenomenas. I kinda feel that relativistic description given by QFT is inevitable but things like propagators, Feynman Diagrams and renomalization... So if someone could explain me what this necessity or council one introduction to the subject. Thanks a lot.

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#### ZapperZ

Staff Emeritus
2018 Award
I am currently following a course of condensed matter physics and quite enjoying it. But after doig some research I found that many book deal with QFT applied to condensed matter. I wonder what all the calculus of QFT is needed to describe those phenomenas. I kinda feel that relativistic description given by QFT is inevitable but things like propagators, Feynman Diagrams and renomalization... So if someone could explain me what this necessity or council one introduction to the subject. Thanks a lot.
Read Mattuck's "A guide to Feynman diagrams in the many-body problem", and you'll have an idea why.

Zz.

#### IRobot

I will take a look at it ;)

thanks for fast responding

#### atyy

In classical physics, you can represent the shape of an infinite chain of particles connected by springs as the amplitudes as each particle, or equivalently as the sum of its modes, where each mode is a collective motion of particles.

In non-relativistic quantum mechanics, you can write the Schroedinger equation for all the particles, or you can write an equivalent equation for its modes. The QFT formalism ("second quantization") does the latter, and is completely equivalent to the former.

http://www.tcm.phy.cam.ac.uk/~bds10/tp3.html
http://www.physics.rutgers.edu/~coleman/620/mbody/pdf/bkx.pdf [Broken]

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