Spektralfunktionen

Spektralfunktionen, also known as spectral functions, are mathematical objects used in quantum field theory and condensed matter physics to describe the distribution of energy or momentum in a system. They are typically defined as vacuum expectation values of time-ordered products of field operators. The spectral function provides information about the possible excitations or particles that can be created from the vacuum state.

In essence, a spectral function acts like a density of states for a given quantity, such as energy. For a system in thermal equilibrium, the spectral function at a specific frequency or momentum can reveal the presence of quasiparticles, collective excitations, or other emergent phenomena. The shape and position of peaks in a spectral function indicate the energies and lifetimes of these excitations.

Mathematically, spectral functions are often represented as integrals involving delta functions, where the delta function signifies a sharp peak at a particular energy or momentum, corresponding to a stable particle or excitation. Broader peaks suggest unstable particles or more complex excitations with shorter lifetimes.

The concept of spectral functions is crucial for understanding various physical phenomena, including scattering processes, transport properties, and the behavior of matter at extreme conditions. They are a powerful tool for connecting theoretical models to experimental observations, allowing physicists to interpret data and gain deeper insights into the fundamental nature of physical systems.