QFT和QM的区别

Differences between QFT and QM

1. Theoretical Framework and Scope - QM - Scope：Primarily used to study the behavior of microscopic particles such as electrons, protons, and atoms. - Objects of Description：Individual particles' motion, energy, wave functions, etc. - Fundamental Principles：Based on Schrödinger's equation, the probabilistic interpretation of the wave function, and the uncertainty principle. - QFT - Scope： Used to describe interactions between particles, especially in high-energy physics, addressing fundamental particles and forces. - Objects of Description：The relationship between fields and particles, where particles are seen as excitations of the underlying fields. - Fundamental PrinciplesBased on the quantization of fields, covering electromagnetic fields, strong interactions, weak interactions, etc.

2. Mathematical Tools and Methods - QM - Uses wave functions (or state vectors) to describe particle states. - Employs Schrödinger's equation or Heisenberg's matrix mechanics to describe the evolution of particles. - QFT - Utilizes field operators(\(\Psi(\boldsymbol{r})\)) to describe the quantum states of fields. - Applies Lagrangians, Hamiltonians, and path integrals to describe the evolution and interactions of fields.

3. Concept of Particles and Fields - QM - Particles are described by the probability density of wave functions, exhibiting wave-particle duality. - Focuses on the motion, energy states, and evolution of particles' wave functions. - QFT - Particles are described as excitations of quantum fields, e.g., the electron field's quantum excitations are electrons. - Emphasizes the quantization of fields, where different types of fields correspond to different particles.

4. Relativity - QM - Generally deals with non-relativistic cases, where particles' velocities are much less than the speed of light. - Relativistic quantum mechanics (like the Dirac equation) is an extension but does not fully encompass relativistic effects. - QFT - Fully compatible with relativity, handling relativistic particles and interactions at high energies. - For example, Quantum Electrodynamics (QED) describes electromagnetic interactions within a relativistic quantum field framework.

5. Application Areas - QM - Mainly applied in atomic physics, molecular physics, condensed matter physics, quantum information, etc. - Describes the electronic structure and energy levels within atoms, molecules, and solids. - QFT - Primarily applied in high-energy physics, particle physics, and cosmology. - Describes the fundamental particles and forces, such as the electromagnetic force, strong force, and weak force.