Feynman Rules Feynman Diagrams Feynman Parametrization Feynman Gauge Feynman Cut-off Feynman...

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Transcript of Feynman Rules Feynman Diagrams Feynman Parametrization Feynman Gauge Feynman Cut-off Feynman...

Page 1: Feynman Rules Feynman Diagrams Feynman Parametrization Feynman Gauge Feynman Cut-off Feynman Propagator Feynman Path integral Feynman Parton Model ….
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• Feynman Rules• Feynman Diagrams• Feynman Parametrization• Feynman Gauge• Feynman Cut-off• Feynman Propagator• Feynman Path integral• Feynman Parton Model• ….

Feynman invented the language of modern particle physics – Feynman diagrams and covariant Feynman rules

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"for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles“

Sin-Itiro Tomonaga Julian Schwinger Richard P. Feynman

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What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it... That is because I don't understand it. Nobody does.QED, The Strange Theory of Light and Matter, (London, 1990) 9.

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it... That is because I don't understand it. Nobody does.QED, The Strange Theory of Light and Matter, (London, 1990) 9.

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.The Character of Physical Law

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.The Character of Physical Law

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Flying photon Flying Electron Flying Positron

2 2

p̂ m

p m ii

2 2

p̂ m

p m ii

2

gip

Emitted photon

Absorbed photon

Emitted electron (absorbed positron)

Absorbed electron (emitted positron)

v

v“I took the observation that positrons couldsimply be represented as electrons goingfrom the future to the past in a back sectionof their world lines” R.Feynman, Nobel Lecture

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Absorption of a photon by an electron

Emission of a photon by an electron

e e

e e

Annihilation

e

All physical processes in Quantum Electrodynamics can be constructed from these elements like LEGO structures

Interaction between electron, positrons and photons

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Compton Scattering Mueller Scattering Annihilation

2( )g

v v i v vp

ˆ( )v p m v

Amplitudes of probability = M

Probability = |M|2

pp

p

2 2p m

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Electrons (e-) and positrons (e+) collide at accelerators at very high energy and produce a pair of muons (μ+ μ-)

v=0. 999 999 999 987 c

LEP Accelerator

N Flux Number of events Cross-section

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2 2 2

2 2 2

22

21 (1 ) (1 )cos

4m m m

E E E

d

d E

2 2 2

2 2 2

22

21 (1 ) (1 )cos

4m m m

E E E

d

d E

2 2

2 2

2122

41 1

3m m

E EE

2 2

2 2

2122

41 1

3m m

E EE

2 22

| | | ( ) |g

M v v i v vp

2 2

2| | | ( ) |

gM v v i v v

p

22 2

1 | | 1| |

2 16 4 spin

d kM

d E E

2

2 2

1 | | 1| |

2 16 4 spin

d kM

d E E

Matrix element

Cross-section

Total x-section

Angular Deps

E=EnergyΩ = Angle

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If I could explain it to the average person, I wouldn't have been worth the Nobel Prize. R.Feynman

Area view of the Large Hadron Collider (CERN)

27 km ring

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"The electron does anything it likes," he said. "It just goes in any direction at any speed, forward or backward in time, however it likes, and then you add up the amplitudes and it gives you the wave-function." I said to him, "You're crazy." But he wasn't.

Freeman J.Dyson, 1983

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The most baffling part of this experiment comes when only one photon at a time is fired at the barrier with both slits open. The pattern of interference remains the same as can be seen if many photons are emitted one at a time and recorded on the same sheet of photographic film. The clear implication is that something with a wavelike nature passes simultaneously through both slits and interferes with itself — even though there is only one photon present. (The experiment works with electrons, atoms, and even some molecules too.)

Feynman was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment.

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“I don't know why this is - it remains a mystery, but it was something I `learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature”. . R.Feynman

The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed. A. Einstein

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Some people say, "How can you live without knowing?" I do not know what they mean. I always live without knowing. That is easy. How you get to know is what I want to know.

I learned very early the difference between knowing the name of something and knowing something.

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If it turns out there is a simple ultimate law which explains everything, so be it — that would be very nice to discover. If it turns out it's like an onion with millions of layers... then that's the way it is. R.Feynman

The Feynman Problem-Solving Algorithm:  (1) write down the problem;  (2) think very hard;  (3) write down the answer.

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Physics isn't the most important thing. Love is.

The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to.

No problem is too small or too trivial if we can really do something about it.

The wonderful thing about science is that it's alive.

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He is by all odds the most brilliant young physicist here, and everyone knows this. J.Oppenheimer on Feynman's status among the physicists at Los Alamos.