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Quantum-Mechanics (11)

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Interacting Field Theory: Time-ordered Green's Function

Dec 30, 2018
14 minutes read

We will introduce the basic Field Theory with interaction considered, which is the main propose of Field Theory actually. We will use the perturbation theory here. And what can we talk is only perturbation-property of Field theory. Our goal is to show the constraint of the form of Lagrangian in Interacting Field Theory. Then we will show the perturbation expansion of the time-ordered Green's function and the corresponding method: Feynman Diagram and Feynman Rules. Green's Function is widely used in field theory, especially in condensed matter theory. But in QFT we just care the connection between it and scattering theory, which will be discussed in next section.

Quantization of Free Field: Maxwell Field

Dec 26, 2018
11 minutes read

The canonical quantization of vector Field(Maxwell Field). One can find that the usual quantization procedure(directly using of commutation relationship) does not work for it, because of the Gauge Symmetry. We will introduce the Gupta-Bleuler quantization procedure. It clearly keeps the Lorentz covariance but leads to a Hilbert space with negative matric. For free Maxwell field we can separate them totally, so the probability interpretation will not destroyed. Then we will computation of propagator and do some discussion. At last we will discuss the discrete symmetry of Maxwell Field in Quantum Theory

Introduction to Relativistic Quantum Mechanics

Dec 24, 2018
14 minutes read

The simple introduction to Relativistic Quantum Mechanics. Mainly about the Dirac equation. Gives some basic understanding about the Dirac equation(in Dirac representation). Get to know some basic consequences of Dirac equation: Orbital angular momentum is not conserved, but the total angular momentum; Zeeman coupling term with g factor is 2; Spin-orbit coupling term and Zitterbewegung: Dirac particle cannot be "at rest" in classical sense. Even with zero momentum and without external potential, it seems to be oscillating.

Quantum-Mechanics