📚 Feynman Diagrams | 费曼图
Feynman diagrams are pictorial representations of the interactions between subatomic particles, invented by Richard Feynman in the 1940s. They serve as intuitive tools to visualise and calculate the probability amplitudes of quantum processes, and are a cornerstone of modern particle physics within the IB syllabus.
费曼图是亚原子粒子间相互作用的图形化表示，由理查德·费曼于 20 世纪 40 年代发明。它们是直观可视化和计算量子过程概率幅的工具，也是 IB 课程中现代粒子物理学的基石。
1. Introduction to Feynman Diagrams | 费曼图简介
A Feynman diagram is a spacetime graph where time typically runs from left to right (or sometimes bottom to top, depending on convention). Straight lines represent fermions (matter particles) and wavy or dashed lines represent bosons (force carriers).
费曼图是一种时空图，通常时间轴从左向右（或有时自下而上，取决于惯例）。实线代表费米子（物质粒子），波浪线或虚线代表玻色子（力的载体）。
Each diagram corresponds to a mathematical expression for a quantum amplitude. The more complex the diagram, the smaller its contribution to the overall probability, because each vertex introduces a coupling constant factor.
每个图对应一个量子振幅的数学表达式。图越复杂，对总概率的贡献越小，因为每个顶点都会引入一个耦合常数因子。
In IB Physics, you do not need to calculate amplitudes; you only need to draw and interpret simple diagrams, identifying particles and conservation laws.
在 IB 物理中，你不需要计算振幅；只需绘制和解释简单图表，识别粒子并应用守恒定律。
2. Axes and Conventions | 坐标轴与惯例
In most IB texts, the x-axis represents space and the y-axis represents time (or vice versa, but the horizontal axis is usually time). Arrows on fermion lines indicate the direction of particle flow, while for antiparticles the arrow points backward in time.
在大多数 IB 教材中，x 轴表示空间，y 轴表示时间（或反之，但水平轴通常是时间）。费米子线上的箭头表示粒子流动方向，而反粒子的箭头指向时间反方向。
A common convention is: time on the horizontal axis, space on the vertical axis. Electron lines are drawn with an arrow pointing to the right for electrons and to the left for positrons (anti-electrons).
常见的惯例是：水平轴为时间，垂直轴为空间。电子线箭头向右表示电子，向左表示正电子（反电子）。
Photons, gluons, and weak bosons are shown as wavy, curly, or dashed lines without arrows, since they are their own antiparticles.
光子、胶子和弱玻色子用波浪线、螺旋线或虚线表示，且不加箭头，因为它们是自身的反粒子。
3. Particles and Lines | 粒子与线
Fermions (quarks and leptons) are represented by straight solid lines. Each fermion line carries an arrow. For a particle (matter), the arrow points forward in time; for an antiparticle, it points backward.
费米子（夸克和轻子）用实直线表示。每条费米子线都带有箭头。对于粒子（物质），箭头指向时间前进方向；对于反粒子，箭头指向时间倒退方向。
Bosons are drawn as: photon – wavy line; gluon – curly line; W⁺, W⁻, Z⁰ – dashed or wavy line often labelled. The Higgs boson may be shown as a dashed line.
玻色子的画法：光子 – 波浪线；胶子 – 螺旋线；W⁺、W⁻、Z⁰ – 虚线或波浪线，通常加标签。希格斯玻色子可用虚线表示。
In IB exams, you might see gluons depicted as a spring-like line and weak bosons as a dashed line with a ‘W’ or ‘Z’ label.
在 IB 考试中，你可能会看到胶子画成弹簧状线，弱玻色子画成虚线并标有 ‘W’ 或 ‘Z’。
4. Vertices and Interactions | 顶点与相互作用
An interaction vertex is a point where a fermion line and a boson line meet (along with another fermion line). The vertex represents the emission or absorption of a boson by a fermion.
相互作用顶点是费米子线与玻色子线（以及另一条费米子线）相遇的点。顶点表示费米子发射或吸收一个玻色子。
Three-particle vertices are the most fundamental building blocks. For example, an electron can emit a photon: e⁻ → e⁻ + γ, or absorb one. The electric charge is conserved at every vertex.
三粒子顶点是最基本的构成单元。例如，电子可以发射一个光子：e⁻ → e⁻ + γ，或吸收一个。电荷在每个顶点处守恒。
Vertices never change the type of lepton (electron cannot turn into a muon via photon emission), but weak vertices can change quark flavour (e.g., d → u + W⁻).
顶点不会改变轻子种类（电子不能通过发射光子变成 μ 子），但弱作用顶点可改变夸克味（如 d → u + W⁻）。
5. Exchange Particles (Bosons) | 交换粒子（玻色子）
Forces are mediated by the exchange of gauge bosons. The electromagnetic force is carried by photons, the weak force by W⁺, W⁻, Z⁰ bosons, and the strong force by gluons.
力由规范玻色子的交换来传递。电磁力由光子承载，弱力由 W⁺、W⁻、Z⁰ 玻色子承载，强力由胶子承载。
In a Feynman diagram, the exchange particle appears as an internal line connecting two vertices. This boson is virtual, meaning it does not satisfy the usual energy–momentum relation E² = p²c² + m²c⁴.
在费曼图中，交换粒子表现为连接两个顶点的内部线。这个玻色子是虚的，意味着它不满足通常的能量–动量关系 E² = p²c² + m²c⁴。
The mass of the exchange boson determines the range of the force: photons (massless) give infinite range; W/Z bosons (heavy) give short-range weak force; gluons (massless) mediate short-range strong force due to colour confinement.
交换玻色子的质量决定力的作用范围：光子（无质量）产生无限作用范围；W/Z 玻色子（质量大）产生短程弱力；胶子（无质量）因色禁闭而传递短程强力。
6. Electromagnetic Interactions (QED) | 电磁相互作用（量子电动力学）
Quantum Electrodynamics (QED) describes how charged particles interact via photon exchange. A classic example is electron–electron scattering (Møller scattering), where two electrons repel by exchanging a virtual photon.
量子电动力学（QED）描述带电粒子如何通过光子交换相互作用。经典例子是电子–电子散射（莫勒散射），两个电子通过交换虚光子而相互排斥。
The Feynman diagram for this process shows two incoming e⁻ lines, a photon wavy line between them, and two outgoing e⁻ lines. The vertex factor is proportional to the electron charge e (fine-structure constant √α).
该过程的费曼图显示两条入射 e⁻ 线、它们之间的一条光子波浪线，以及两条出射 e⁻ 线。顶点因子正比于电子电荷 e（精细结构常数 √α）。
Electron–positron annihilation into two photons (e⁻ + e⁺ → γ + γ) is another standard IB diagram. Here, the fermion lines meet at a vertex with the arrow on the e⁺ line pointing backward in time.
电子–正电子湮灭成两个光子（e⁻ + e⁺ → γ + γ）是另一个标准的 IB 图。这里，费米子线在顶点相遇，e⁺ 线的箭头指向时间反方向。
7. Weak Interactions | 弱相互作用
Weak interactions are responsible for processes like beta decay. In β⁻ decay, a down quark in a neutron changes into an up quark, emitting a W⁻ boson, which then decays into an electron and an electron antineutrino: d → u + W⁻, then W⁻ → e⁻ + ν̄ₑ.
弱相互作用负责诸如 β 衰变等过程。在 β⁻ 衰变中，中子内的一个下夸克变为上夸克，发射一个 W⁻ 玻色子，然后 W⁻ 衰变为一个电子和一个反电子中微子：d → u + W⁻，然后 W⁻ → e⁻ + ν̄ₑ。
The corresponding Feynman diagram has a neutron line splitting into a proton line and a W⁻ boson line; the W⁻ then splits into an electron line (with arrow forward) and an antineutrino line (arrow backward).
相应的费曼图有一条中子线分叉为一条质子线和一条 W⁻ 玻色子线；W⁻ 接着再分叉为一条电子线（箭头向前）和一条反中微子线（箭头向后）。
For β⁺ decay, a proton (uud) converts into a neutron (udd) by u → d + W⁺, and W⁺ → e⁺ + νₑ. The positron has an arrow pointing backward in time.
对于 β⁺ 衰变，质子（uud）通过 u → d + W⁺ 转化为中子（udd），且 W⁺ → e⁺ + νₑ。正电子的箭头指向时间反方向。
8. Strong Interactions | 强相互作用
Strong interactions bind quarks together inside hadrons via gluon exchange. A simple Feynman diagram for a quark–quark interaction shows two quark lines exchanging a curly gluon line.
强力通过胶子交换将夸克束缚在强子内部。一个简单的夸克–夸克相互作用费曼图显示两条夸克线交换一条螺旋状胶子线。
Because gluons carry colour charge, they can also interact with each other, leading to three-gluon and four-gluon vertices. These are not typically required in IB but illustrate the complexity of Quantum Chromodynamics (QCD).
由于胶子携带色荷，它们之间也能相互作用，产生三胶子和四胶子顶点。这些通常不在 IB 要求范围内，但展示了量子色动力学（QCD）的复杂性。
A classic IB diagram for strong interaction is pion (π⁺) exchange between a proton and a neutron, though this is an effective description at low energy; at a fundamental level it’s gluon exchange between quarks.
IB 中经典的强相互作用图是质子和中子之间的 π⁺ 介子交换，尽管这是低能下的有效描述；本质上仍是夸克间的胶子交换。
9. Feynman Diagram Rules and Conservation Laws | 费曼图规则和守恒定律
At each vertex, electric charge, lepton number, baryon number, and colour charge (for strong vertices) must be conserved. Weak vertices must also conserve total lepton number separately for each generation, though flavour may change.
在每个顶点，电荷、轻子数、重子数和色荷（对于强顶点）必须守恒。弱顶点也必须分别守恒各代的轻子总数，尽管味可能会改变。
Energy and momentum are conserved overall for the process, but a virtual particle may temporarily ‘violate’ energy conservation within the limits of the Heisenberg uncertainty principle ΔE Δt ≥ ħ/2.
过程总体能量和动量守恒，但虚粒子可在海森堡不确定性原理 ΔE Δt ≥ ħ/2 的限制下暂时 ‘违反’ 能量守恒。
When drawing Feynman diagrams, always check that the total charge and lepton/baryon numbers on the left equal those on the right (including any internal virtual particles cancelling out).
绘制费曼图时，务必检查左侧的总电荷、轻子/重子数与右侧相等（包括内部虚粒子的抵消）。
10. Virtual Particles | 虚粒子
Virtual particles are internal lines in Feynman diagrams that are not directly observable. They exist only for a very short time, borrowing energy from the vacuum according to the uncertainty relation.
虚粒子是费曼图中不可直接观察的内部线。它们仅存在极短时间，根据不确定性关系从真空中借用能量。
The mass of a virtual particle can be off-shell (not equal to its free-particle mass). For example, a virtual photon can have mass ≠ 0, which is why the electromagnetic force can be attractive or repulsive.
虚粒子的质量可以离壳（不等于其自由粒子质量）。例如，虚光子可以有非零质量，这就是电磁力既可吸引也可排斥的原因。
The greater the mass of the virtual boson, the shorter the lifetime allowed by Δt ≈ ħ/ΔE, so short-range forces are mediated by heavy virtual bosons.
虚玻色子的质量越大，Δt ≈ ħ/ΔE 允许的寿命越短，因此短程力由大质量虚玻色子传递。
11. Drawing and Interpreting Feynman Diagrams | 绘制与解读费曼图
To draw a Feynman diagram, start by identifying the initial and final state particles. Connect them using the appropriate interaction vertices and internal exchange boson, respecting all conservation laws.
要绘制费曼图，首先确定初态和末态粒子。用适当的相互作用顶点和内部交换玻色子连接它们，同时遵守所有守恒定律。
Label each line clearly, especially for weak bosons (W⁺, W⁻, Z⁰). Arrows on fermion lines must be consistent with particle/antiparticle flow. Time direction should be indicated.
清晰标记每条线，特别是弱玻色子（W⁺, W⁻, Z⁰）。费米子线上的箭头必须与粒子/反粒子流向一致。应标出时间方向。
Interpreting a given diagram: identify the interaction type (EM, weak, or strong) by looking at the exchange boson. Then deduce the process by following lines from initial to final states.
解读给定图：通过观察交换玻色子确定相互作用类型（电磁、弱或强）。然后跟随从初态到末态的线来推导过程。
12. IB Exam Tips | IB 考试技巧
IB Physics exam questions often ask you to draw a Feynman diagram for a given process, such as β⁻ decay or electron–positron annihilation. Practice drawing clear, well-labelled diagrams with a ruler.
IB 物理考题常要求你绘制给定过程的费曼图，如 β⁻ 衰变或电子–正电子湮灭。练习用尺子画出清晰、标注明确的图。
You may be asked to identify the exchange particle in a diagram, or state why a particular diagram is forbidden (e.g., violates charge conservation). Always check charges and lepton numbers first.
你可能会被要求识别图中的交换粒子，或说明某个图为什么被禁止（例如违反电荷守恒）。总是先检查电荷和轻子数。
Multiple-choice questions might present a Feynman diagram and ask which interaction is represented. Remember: photon → EM; W/Z → weak; gluon → strong. Virtual particles are internal lines only.
选择题可能给出一个费曼图，问表示哪种相互作用。记住：光子 → 电磁；W/Z → 弱；胶子 → 强。虚粒子只是内部线。
When explaining, use correct terminology (vertex, virtual, exchange boson) and relate to conservation laws. Even if you cannot calculate the amplitude, a qualitative description can earn marks.
解释时使用正确术语（顶点、虚、交换玻色子）并结合守恒定律。即使不会计算振幅，定性描述也能得分。
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