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# 物理代写|凝聚态物理代写Condensed Matter Physics代考|PHYS451 Graphical representation of elementary excitations and probe particles

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## 物理代写|凝聚态物理代写Condensed Matter Physics代考|Graphical representation of elementary excitations and probe particles

Elementary excitations, probe particles, and their interactions can be represented graphically (Feynman diagrams). When describing physical processes, it is often assumed that time develops from the left to the right, or from the bottom to the top of the diagram used to describe the process. Each elementary excitation or probe particle is depicted by a line (a different type of line for each type of excitation) and a label that characterizes its quantum numbers. Some graphic representations are shown in Fig. 1.5.

## 物理代写|凝聚态物理代写Condensed Matter Physics代考|Quasiparticle–boson interactions

Many physical processes in condensed matter systems involve the interactions of quasiparticles with bosons. The bosons may correspond to the collective excitations of the system or to the probe particles. Some examples are given in Fig. 1.6, where electrons and holes are used as the prototypes for the quasiparticles, and photons represent bosons. The following cases are given graphically in Fig. 1.6: (a) an electron having wavevector k emits a photon of wavevector $-\mathbf{q}$ and is scattered into a state described by wavevection $\mathbf{k}+\mathbf{q}$; (b) an electron with wavevector $\mathbf{k}$ absorbs a photon of wavevector $\mathbf{q}$ and is scattered into a state $\mathbf{k}+\mathbf{q}$; (c) a hole with wavevector $-\mathbf{k}-\mathbf{q}$ emits a photon at wavevector $-\mathbf{q}$ and is scattered into the state $-\mathbf{k}$; (d) a hole of wavevector $-\mathbf{k}-\mathbf{q}$ absorbs a photon of wavevector $\mathbf{q}$ and is scattered into the state $-\mathbf{k}$; (e) the creation of an electron of wavevector $\mathbf{k}+\mathbf{q}$ and a hole of wavevector $-\mathbf{k}$ by a photon of wavevector $\mathbf{q}$; and (f) the annihilation of an electron of wavevector $\mathbf{k}+\mathbf{q}$ and a hole of wavevector $-\mathbf{k}$ to produce a photon of wavevector $\mathbf{q}$.
The photon representing the boson in Fig. $1.6$ can be replaced by other bosons. Examples of common electron-boson interactions are shown in Fig. 1.7. These include the electron-photon interaction and others, such as the electron-phonon interaction and the electron-plasmon interaction. In each of these examples an electron with wavevector $\mathbf{k}$ emits a boson of wavevector $\mathbf{q}$ and is scattered into a state described by wavevector $\mathbf{k}-\mathbf{q}$

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