# Calculate something with QFT - I dare you

## Main Question or Discussion Point

Sort of kidding with the title here. But seriously I am having trouble making progress in my study of QFT because I can't see where it is going. Please give me an example of something to calculate with QFT that corresponds to a measurable quantity, hopefully something which cannot be calculated with regular QM (non-relativistic or relativistic).

No computational details required. I'll look it up and figure it out myself. But right now I'm like learning to read musical notation without ever having heard music.

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The S-matrix for electron-electron scattering.

Decay rate of a pion, or cross-section for scattering electrons off of eachother.

nrqed
Homework Helper
Gold Member
Sort of kidding with the title here. But seriously I am having trouble making progress in my study of QFT because I can't see where it is going. Please give me an example of something to calculate with QFT that corresponds to a measurable quantity, hopefully something which cannot be calculated with regular QM (non-relativistic or relativistic).

No computational details required. I'll look it up and figure it out myself. But right now I'm like learning to read musical notation without ever having heard music.
What reference are you using? You should be able to find worked out examples in any book on QFT.

A calculation in QFT has many steps. There is all the framework to get from the S-matrix to the the Feynman rules and how they are related to observables. It's easy to lose track of the forest from the trees here. A nice summary is https://www.physicsforums.com/showthread.php?t=212335

But I personally think that it's better to first set aside all the heavy formalism and to accept the Feynman rules and practice calculating some observables. After this is mastered, one can go back and see where the Feynman rules come from.

Electron-muon scattering ( $$e^- \mu^- \rightarrow e^- \mu^-$$), cross section. Cross section for $$e^+ e^- \rightarrow \mu^+ \mu^-$$, cross section for $$e^+ e^- \rightarrow e^+ e^-$$.

These examples give some practice with QED and spinor trace calculations.

Then the next obvious thing to calculate is the decay rate of a muon.

A nice book for those simple examples is Halzen and Martin but almost any QFT book would do them.

nrqed
Homework Helper
Gold Member
What reference are you using? You should be able to find worked out examples in any book on QFT.

A calculation in QFT has many steps. There is all the framework to get from the S-matrix to the the Feynman rules and how they are related to observables. It's easy to lose track of the forest from the trees here. A nice summary is https://www.physicsforums.com/showthread.php?t=212335

But I personally think that it's better to first set aside all the heavy formalism and to accept the Feynman rules and practice calculating some observables. After this is mastered, one can go back and see where the Feynman rules come from.

Electron-muon scattering ( $$e^- \mu^- \rightarrow e^- \mu^-$$), cross section. Cross section for $$e^+ e^- \rightarrow \mu^+ \mu^-$$, cross section for $$e^+ e^- \rightarrow e^+ e^-$$.

These examples give some practice with QED and spinor trace calculations.

Then the next obvious thing to calculate is the decay rate of a muon.

A nice book for those simple examples is Halzen and Martin but almost any QFT book would do them.
Strange...I can't edit my posts?!

(EDIT: Oh, ok. Yes I can edit, the chance to edit does not last very long, that's all.)

Anyway,

To add to my previous post, the next thing to calculate could be the one-loop contribution to the anomalous magnetic moment of the electron, the famous alpha/(2 pi) term. This would give an idea of a one-loop calculation.

Of course, a nice thing to try is a QCD tree level calculation which gives some practice with non-abelian matrices. Unfortunately, the connection to actual observables requires a bit more work here.

A nice book for those simple examples is Halzen and Martin but almost any QFT book would do them.
You mean Quarks and Leptons: An Introductory Course in Modern Particle Physics , right?

What reference are you using?
Quite a few. I read one, scratch my head, and then look at the next. I'll try Halzen and Martin. If I'm still scratching, Head and Shoulders is next.

nrqed
Homework Helper
Gold Member
You mean Quarks and Leptons: An Introductory Course in Modern Particle Physics , right?

Quite a few. I read one, scratch my head, and then look at the next. I'll try Halzen and Martin. If I'm still scratching, Head and Shoulders is next.
Yes that's the book I meant. I loved it when I first learned particle physics because they went right to the application: using Feynman diagrams to get an observable quantity. They show very clearly how to do that.

A lot of people might find this very unsatisfactory because they might react by saying "but where do these Feynman rules come from?". This is where a QFT book will come in. I guess it depends on one's personality. I like to see what things are used for before learning the gritty technical details. Some people prefer to see everything build up from the ground up but in th ecase of QFT that means a lot of background before getting to "the point".

I personally preferred Griffiths over Halzen & Martin, but they are roughly at the same level. Griffiths calculates cross sections and decay rates from a toy-model quantum field theory which makes it very easy to see how these numbers are related to the feynman rules for a theory. He then goes on to state the Feynman rules for QED, QCD etc.

Then you can read a QFT text which derives Feynman rules for any given Lagrangian; this is, as you probably know, quite a mess of different topics but satisfying to know. A good QFT text will also show you how Lagrangians can be constructed by making them satisfy certain symmetries (Poincaré and gauge symmetries). A text will also describe the standard model arising from the U(1) x SU(2) x SU(3) gauge group, and this will fit in with all you know about CKM matrices and stuff from your particle physics studies.

A next step is supersymmetry and this relies on you knowing in detail about Poincaré symmetry and representations of the Poincaré group etc.

Try the Introduction to QFT by Maggiore.

Hans de Vries
Gold Member
The pragmatic path is indeed Griffiths and Halzen & Martin, you'll learn the stuff which
leads to real results. Halzen & Martin go a few steps further as Griffiths.

Zee is then a good intro into the path integral mechanism and how it leads to series
of Feynman diagrams.

Ryder handles the various aspects of QED and QFT but nicely separated into different
chapters.

P&S is more along the line of Coleman's style which freely mixes all kinds of subjects
all the time: propagators, 2nd order quantization, Heisenberg and Schrödinger picture,
relativistic and non-relativistic physics. It look impressive but it mixes subjects
with varying experimental status and mixing relativistic with non-relativistic physics
makes a mess in my opinion.

P&S's treatment of the Dirac equation is actually very good but unfortunately much
to compact. The book becomes much more practically useful in the later chapters.

Regards, Hans

Turns out I have Griffiths on my shelf. Bought it 15 years ago. Probably I'll be back with questions in a week or so.

thanks for the recommends.

Todd

[P&S] look impressive but it mixes subjects
with varying experimental status and mixing relativistic with non-relativistic physics
makes a mess in my opinion.

I agree.

reilly