📚 Feynman Diagrams: Understanding and Applications in IB Physics | 费曼图的理解与应用
Feynman diagrams are a visual language used in particle physics to represent how particles interact by exchanging virtual bosons. They were introduced by Richard Feynman in the 1940s and have since become one of the most powerful tools in the Standard Model. For IB Physics HL students, Feynman diagrams appear in the particle physics topic and are used to explain interactions such as electron scattering, beta decay and quark interactions.
费曼图是粒子物理学中一种可视化的“语言”，用来表示粒子如何通过交换虚玻色子发生相互作用。它由理查德·费曼于20世纪40年代提出，从此成为标准模型中最有力的工具之一。对IB物理HL学生而言，费曼图出现在粒子物理部分，用于解释电子散射、β衰变和夸克相互作用等过程。
1. What Are Feynman Diagrams? | 什么是费曼图？
A Feynman diagram is a spacetime diagram showing the initial particles on the left, the final particles on the right, and the interaction taking place in between. Each line represents the worldline of a particle; each vertex represents an interaction. In advanced physics, each diagram can be converted into a mathematical expression that contributes to the probability amplitude of a process.
费曼图是一种时空图：初态粒子画在左侧，末态粒子画在右侧，相互作用发生在中间。每一条线代表一个粒子的“世界线”，每一个顶点代表一次基本相互作用。在高等物理中，每个费曼图都可以转换为一个数学表达式，从而贡献到某个过程的概率幅。
In IB Physics, you do not need to perform full calculations. Instead, you should be able to draw simple diagrams, identify the exchange particle, and use conservation laws to check whether a diagram is physically possible.
在IB物理中，你不需要进行完整的计算，而是应该会画出简单的费曼图、识别交换粒子，并能利用守恒定律判断一个图在物理上是否可能。
2. The Building Blocks: Lines and Vertices | 基本构件：线、顶点与交换粒子
Every Feynman diagram is built from a small number of elements. The most common types of lines are shown below.
每一个费曼图都由有限的几种基本元素构成。最常见的线段类型如下。
- Fermion lines (solid straight lines with arrows): quarks and leptons. If time flows left to right, an arrow pointing right means a particle; an arrow pointing left means an antiparticle.
- Photon and weak bosons (wavy or dashed lines): γ, W⁺, W⁻ and Z⁰ are exchange particles.
- Gluon lines (coiled or loop lines): exchange particles of the strong interaction.
- Vertices: points where one fermion line emits/absorbs a boson, or where a boson converts into a pair.
费米子线：实直线加箭头。若时间轴从左向右，箭头向右表示粒子，箭头向左表示反粒子。光子与弱玻色子用波浪线或虚线表示，如γ、W⁺、W⁻、Z⁰。胶子线通常用螺旋线表示。顶点是费米子发射或吸收玻色子的点，也可以是一个玻色子转化为正反粒子对的点。
| Interaction | Exchange particle | Example |
| Electromagnetic | γ (photon) | electron-electron scattering |
| Weak | W⁺, W⁻, Z⁰ | beta decay |
| Strong | g (gluon) | quark-quark force inside a proton |
3. Reading Time and Space Direction | 时间轴与空间方向
By convention in IB Physics, time flows from left to right. Therefore particles entering from the left are the initial state, and particles leaving to the right are the final state. The vertical axis represents space, but it is not drawn to scale.
按照IB物理中的约定，时间从左向右流动。因此，从左侧进入的粒子是初态，向右离开的粒子是末态。纵轴代表空间，但图中并不按比例绘制。
An external line touches the edge of the diagram and represents a real, observable particle. An internal line, drawn between two vertices, represents a virtual particle that exists only during the interaction. Virtual particles cannot be detected directly because according to the energy-time uncertainty relation, they exist for too short a time.
外线伸到图的最外侧，代表真实可观测的粒子。内线连接两个顶点，代表只在相互作用过程中存在的虚粒子。虚粒子无法被直接探测到，因为根据能量-时间不确定关系，它们存在的时间极短。
ΔE Δt ≈ ħ/2
This relation allows a particle to be “off mass shell” for a very short period, meaning it can temporarily have an energy/momentum relationship different from a real particle.
这意味着虚粒子允许在极短时间内“离开质壳”，即其能量和动量之间的关系暂时不符合真实粒子的要求。
4. Electromagnetic Interactions and Virtual Photons | 电磁相互作用与虚光子
The simplest electromagnetic process is the scattering of two charged particles. For example, two electrons can interact by exchanging a virtual photon. One electron emits the photon, the other electron absorbs it, and both electrons continue with different directions and speeds.
最简单的电磁过程是两个带电粒子的散射。例如，两个电子可以通过交换虚光子发生相互作用：一个电子发射虚光子，另一个电子吸收虚光子，之后两者继续运动，方向与速率发生改变。
In a Feynman diagram, this is drawn as two straight electron lines with arrow pointing to the right, joined by a wavy photon line between two vertices. At each vertex, electric charge is conserved: the electron has charge −1 before and after the vertex, and the photon has charge 0.
在费曼图中，这个过程画为两条箭头向右的电子线，中间由一条波浪形的光子线连接两个顶点。在每个顶点处，电荷守恒：电子在顶点前后的电荷都是−1，光子电荷为0。
The strength of electromagnetic interactions is determined by the fine-structure constant:
电磁相互作用的强度由精细结构常数决定：
α = e² / 4πε₀ħc ≈ 1/137
Since α is much smaller than 1, the probability of a single-photon exchange is relatively small, and diagrams with more vertices are increasingly less important.
由于α远小于1，单光子交换的概率相对较小，因此顶点数越多的图贡献会越来越小。
5. Weak Interactions: Beta Decay and Quark Flavour Change | 弱相互作用：β衰变与夸克味变
The weak interaction is the only fundamental force that can change quark flavour. This makes it responsible for beta decay and the production of neutrinos. The charged weak bosons are W⁺ and W⁻; the neutral weak boson is Z⁰.
弱相互作用是唯一能够改变夸克味的基本力。正因如此，它造成了β衰变和中微子的产生。带弱相互作用玻色子为W⁺、W⁻，中性弱玻色子为Z⁰。
Beta-minus decay is: n → p + e⁻
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