Observables in condensed matter (QFT)

[Mr rabbit]

Quantum field theory is a powerful tool to calculate observables given the amplitude of some process.
I only know the application to high energy physics: you have a Lagrangian with an interaction term between some fields, and you can calculate the amplitude of some process. Once you have this amplitude, you can usually calculate two observables: cross sections (scattering processes) and decay widths (decay processes).

How does this work in condensed matter physics? You have a Hamiltonian, you can calculate amplitudes using the perturbation theory ... and then? What kind of observables can you calculate and how do they relate to the amplitude?

 

[ZapperZ]

Whoa! That's a whole course that you're asking!

I suggest you pick up Mattuck's "A Guide To Feynman Diagrams in Many-Body Problems" (Dover). It shows you how the "propagator", i.e. the Green's function, is applied in many-body problem of electron-electron interactions in solids.

Zz.

 

[Entr0pic]

Excellent recommendation by ZapperZ; Mattuck saved my life when I began studying a course on quantum condensed matter physics.

Adding some more detail, quantum field theory manifests in condensed matter physics via the occupation-number formalism (or second quantisation). Essentially, creation and annihilation operators are introduced to add and remove particles in a single particle state (which, in turn, is a component of a many particle wave-function). Second quantisation is a fundamental part of quantum many-body physics.

In this formalism, observables can be represented in terms of creation and annihilation operators. Of course, it'd be boring if we were limited to just electrons and what not, but no worries: creation and annihilation operators can also be used to represent quasiparticles. An excellent example of the use of quantum field theory techniques in condensed matter physics is the famous Bardeen-Cooper-Schrieffer theory of superconductivity.

 

[king vitamin]

A few common observables computed in field theoretical condensed matter physics: spectral functions (the imaginary part of the retarded Green's function corresponding to some operator), linear response (related to certain amplitudes via the Kubo formula), decay widths (for the same reason as in high energy, but you're generally working with quasiparticles), renormalization group equations, bound states and their energies (also possible in high energy physics).

 

[DrDu]

Most one particle properties can be calculated from the one particle Greens function. Energy density from the vacuum propagator. I would not recommend Mattuck, especially since you already know relativistic QFT.
Classics are Fetter Walecka, and "AGD" (Abrikosov, Gorkov, ...). There are also many excellent modern books on the topic.

 

[fluidistic]

Most one particle properties can be calculated from the one particle Greens function. Energy density from the vacuum propagator. I would not recommend Mattuck, especially since you already know relativistic QFT.
Classics are Fetter Walecka, and "AGD" (Abrikosov, Gorkov, ...). There are also many excellent modern books on the topic.

Feel free to mention a few modern books.

 

[king vitamin]

I'm a different poster, but I'll say that some good modern books include: Altland & Simons, Xiao-Gang Wen, and Piers Coleman. Shankar also just wrote a textbook, but I haven't had the chance to check it out (but his other books are excellent so I'd be surprised if it wasn't good).

 

[Mr rabbit]

Thank you for your answers. I will take a look at Mattuck and Piers Coleman then!