# Observables in condensed matter (QFT)

• A
• Mr rabbit
In summary, quantum field theory is a powerful tool used to calculate observables given the amplitude of some process. It manifests in condensed matter physics via the occupation-number formalism. Most one particle properties can be calculated from the one particle Greens function.

#### 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?

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.

Mr rabbit and 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.

Mr rabbit
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).

Mr rabbit
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.

Mr rabbit and fluidistic
DrDu said:
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.

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).

protonsarecool, Mr rabbit and fluidistic
Thank you for your answers. I will take a look at Mattuck and Piers Coleman then!

## 1. What are observables in condensed matter?

Observables in condensed matter refer to physical quantities that can be measured or observed in a condensed matter system. These can include properties such as density, energy, magnetization, and conductivity.

## 2. How are observables described in quantum field theory (QFT)?

In QFT, observables are described as operators on the quantum field. These operators act on the quantum state of the system and represent the physical measurement that can be made on the system.

## 3. What is the significance of observables in condensed matter physics?

Observables play a crucial role in understanding the behavior and properties of condensed matter systems. By measuring these observables, we can gain insight into the underlying quantum field theory and make predictions about the behavior of the system.

## 4. Can observables in condensed matter be measured directly?

In most cases, observables in condensed matter cannot be measured directly. Instead, they are inferred from indirect measurements or theoretical calculations. This is due to the complexity and size of condensed matter systems, making direct measurement difficult.

## 5. How do observables in condensed matter differ from those in other areas of physics?

The observables in condensed matter systems are often different from those in other areas of physics due to the unique properties and behavior of these systems. For example, in particle physics, observables may include particle interactions and decays, while in condensed matter, they may include properties such as phase transitions and collective behavior.