mathematics

John Clayton Taylor

John Clayton Taylor 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 John Clayton Taylor rather than just read about it. In short: John Clayton Taylor (born 4 August 1930) is a British mathematical physicist. He is an Emeritus Professor of Mathematical Physics at the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge and an Emeritus Fellow of Robinson College.

Key takeaways

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

Reference excerpt

John Clayton Taylor (born 4 August 1930) is a British mathematical physicist. He is an Emeritus Professor of Mathematical Physics at the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge and an Emeritus Fellow of Robinson College. He is the father of mathematician Richard Taylor.

Education Taylor earned his PhD degree from the University of Cambridge in 1956, under the supervision of Richard J. Eden and Abdus Salam. His thesis was titled Renormalisation and Related Topics in Quantum Field Theory.

Research Taylor has made contributions to quantum field theory and the physics of elementary particles. His contributions include the discovery (also made independently by Lev Landau) of singularities in the analytical structure of the Feynman integrals for processes in quantum field theory, the PCAC nature of radioactive decay of the pion and the discovery in 1971 of the so-called Slavnov–Taylor identities, which control symmetry and renormalisation of gauge theories. With various collaborators, in 1980 he discovered that real and virtual infrared divergences do not cancel in QCD as they do in QED. They also showed how these infrared divergences exponentiate. In addition, they contributed to the resummation programme in thermal QCD, simplifying the "hard" part of the effective action. Later, they studied complications arising from the non-polynomial nature of the QCD Hamiltonian in the (unitary) Coulomb gauge.

Books Gauge Theories of Weak Interactions (1976) Hidden Unity in Nature's Laws (2001) Gauge Theories in the Twentieth Century (2001)

Awards and honours Taylor was elected a Fellow of the Royal Society (FRS) in 1981. His certificate of election reads: Distinguished for his contributions to the Quantum Theory of Fields and the Physics of Elementary Particles. His important works concern (a) the discovery (also made independently by L.D. Landau) of singularities in the analytical structure of the Feynman integrals for processes in Quantum Field Theory, and (b) the discovery of the so-called Slavnov–Taylor identities in Gauge Theories. He has made significant contributions to Quantum Chromodynamics where his use of the axial gauge has made possible recent advances in "perturbative Q.C.D.". He has also contributed to weak interaction theory, over a long period, and most recently to the elucidation of the gauge structure of the unified weak and electromagnetic interaction.

References

Worked examples

Example 1 — a first encounter with John Clayton Taylor

Start with the simplest possible case. Write down what John Clayton Taylor 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 John Clayton Taylor 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 John Clayton Taylor 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 John Clayton Taylor

In research: John Clayton Taylor 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 John Clayton Taylor 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: John Clayton Taylor is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1930 births, British fellows of the Royal Society, British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John Clayton Taylor 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.

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How to study John Clayton Taylor in 20 minutes

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

Frequently asked questions

What is John Clayton Taylor in simple terms?

Why does John Clayton Taylor 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 John Clayton Taylor?

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 John Clayton Taylor.