physics

One-loop Feynman diagram

One-loop Feynman diagram is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand One-loop Feynman diagram rather than just read about it. In short: In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic). Such a diagram can be obtained from a connected tree diagram by taking two external lines of the same type and joining them together into an edge.

Key takeaways

One-loop Feynman diagram belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect One-loop Feynman diagram to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of One-loop Feynman diagram from memory before moving on to harder problems.

Reference excerpt

In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic). Such a diagram can be obtained from a connected tree diagram by taking two external lines of the same type and joining them together into an edge. Diagrams with loops (in graph theory, these kinds of loops are called cycles, while the word loop is an edge connecting a vertex with itself) correspond to the quantum corrections to the classical field theory. Because one-loop diagrams only contain one cycle, they express the next-to-classical contributions called the semiclassical contributions. One-loop diagrams are usually computed as the integral over one independent momentum that can "run in the cycle". The Casimir effect, Hawking radiation and Lamb shift are examples of phenomena whose theoretical existence can be implied using one-loop Feynman diagrams, especially the well-known "triangle diagram":

The evaluation of one-loop Feynman diagrams usually leads to divergent expressions, which are either due to:

zero-mass particles in the cycle of the diagram (infrared divergence) or insufficient falloff of the integrand for high momenta (ultraviolet divergence). Infrared divergences are usually dealt with by assigning the zero mass particles a small mass λ, evaluating the corresponding expression and then taking the limit λ → 0 {\displaystyle \lambda \to 0} . Ultraviolet divergences are dealt with by renormalization.

See also Tadpole (physics) Furry's theorem

References

Illustrations

Worked examples

Example 1 — a first encounter with One-loop Feynman diagram

Start with the simplest possible case. Write down what One-loop Feynman diagram claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to One-loop Feynman diagram before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about One-loop Feynman diagram ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of One-loop Feynman diagram

In research: One-loop Feynman diagram appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses One-loop Feynman diagram in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: One-loop Feynman diagram is common in secondary-school and first-year university syllabi. It links to neighbouring topics Diagrams, Quantum field theory, Quantum physics stubs, so understanding it makes those chapters shorter.
In everyday life: Look for One-loop Feynman diagram outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study One-loop Feynman diagram in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what One-loop Feynman diagram means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain One-loop Feynman diagram out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is One-loop Feynman diagram in simple terms?

Why does One-loop Feynman diagram matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study One-loop Feynman diagram?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on One-loop Feynman diagram.