mathematics

Landau–Yang theorem

Landau–Yang theorem is a mathematics 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 Landau–Yang theorem rather than just read about it. In short: In quantum mechanics, the Landau–Yang theorem is a selection rule for particles that decay into two on-shell photons. The theorem states that a massive particle with spin 1 cannot decay into two photons.

Key takeaways

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

Reference excerpt

In quantum mechanics, the Landau–Yang theorem is a selection rule for particles that decay into two on-shell photons. The theorem states that a massive particle with spin 1 cannot decay into two photons. It is named after the work of Lev Landau in 1948 and C.N. Yang in 1950.

Assumptions A photon here is any particle with spin 1, without mass and without internal degrees of freedom. The photon is the only known particle with these properties.

Consequences The theorem has several consequences in particle physics. For example:

The ρ meson cannot decay into two photons, differently from the neutral pion, that almost always decays into this final state (98.8% of times). The Z boson cannot decay into two photons. The Higgs boson, whose decay into two photons was observed in 2012, cannot have spin 1 in models that assume the Landau–Yang theorem. Measurements taken in 2013 have since confirmed that the Higgs has spin 0.

Original references

Additional references

Worked examples

Example 1 — a first encounter with Landau–Yang theorem

Start with the simplest possible case. Write down what Landau–Yang theorem claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Landau–Yang theorem 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 Landau–Yang theorem 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 Landau–Yang theorem

In research: Landau–Yang theorem appears in mathematics 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 Landau–Yang theorem 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: Landau–Yang theorem is common in secondary-school and first-year university syllabi. It links to neighbouring topics Lev Landau, Theorems in quantum mechanics, Yang Chen-Ning, so understanding it makes those chapters shorter.
In everyday life: Look for Landau–Yang theorem 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Landau–Yang theorem” →

Affiliate

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

How to study Landau–Yang theorem in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Landau–Yang theorem 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 Landau–Yang theorem out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Landau–Yang theorem in simple terms?

Why does Landau–Yang theorem matter?

Because it connects several mathematics 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 Landau–Yang theorem?

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 Landau–Yang theorem.