Why QFT in condensed matter physics?

In summary, there is a strong connection between quantum field theory and condensed matter physics, and understanding Feynman diagrams is key in exploring this relationship. Mattuck's "A guide to Feynman diagrams in the many-body problem" is a recommended resource for gaining a deeper understanding of this connection. Additionally, the QFT formalism, or "second quantization," is equivalent to classical physics and is important in describing collective motions of particles in condensed matter systems.
  • #1
IRobot
87
0
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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  • #2
IRobot said:
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.
 
  • #3
I will take a look at it ;)

thanks for fast responding
 
  • #4
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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1. Why is QFT used in condensed matter physics?

QFT (Quantum Field Theory) is a powerful mathematical framework for describing the behavior of particles and fields at a microscopic level. In condensed matter physics, this is essential for understanding the behavior of atoms and electrons in materials, as well as their interactions with each other.

2. How does QFT help in studying condensed matter systems?

QFT allows for the description of complex systems with many interacting particles and fields. It also provides a way to calculate and predict the behavior of these systems, which is crucial in understanding condensed matter phenomena such as superconductivity and magnetism.

3. Can classical mechanics be used instead of QFT in condensed matter physics?

While classical mechanics can provide a simpler approximation for some condensed matter systems, it cannot fully capture the quantum effects that are essential for understanding the behavior of materials at a microscopic level. QFT is necessary for accurately describing and predicting the properties of these systems.

4. Are there any limitations to using QFT in condensed matter physics?

Like any scientific theory, QFT has its limitations. It is a relatively complex mathematical framework and can be challenging to apply to certain systems. Also, QFT does not yet have a complete formulation for systems with strong interactions, making it difficult to study some condensed matter phenomena.

5. How has QFT contributed to our understanding of condensed matter physics?

QFT has been instrumental in advancing our understanding of condensed matter physics. It has allowed for the prediction and discovery of new materials, as well as the explanation of various phenomena such as superconductivity and topological states of matter. QFT also provides a unifying framework for connecting different areas of condensed matter physics and has led to many exciting breakthroughs in the field.

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