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Quantum Field Theory
( QFT )

There are things that are not directly observable  [like quantized fields] 
in terms of which we shall have a more fundamental understanding.
Julian Schwinger (1918-1994;Nobel 1965)
 Michon
 
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Related articles on this site:

Related Links (Outside this Site)

LBNL:  The Particle Adventure | QuarkDance | Educational Sites
Contemporary Physics Education Project  (CPEP)  |  QuarkNet
QED of Qubits  by  Iwo Bialynicki-Birula  and Tomasz Sowinski.
QuantumField Theory has no Problems  by  Lubos Motl.
Feynman Diagrams for the Masses  by  Carl Brannen.
Bethe-Salpeter Equation  by  Francesco Sottile.

Textbooks on Quantum Field Theory :  [discussion ]

  • "Relativistic Quantum Fields" James D. Bjorken & Sidney D. Drell  (1965).
  • "Fields" (electronic QFT textbook)  by Warren Siegel  (1999-2005).
  • "Quantum Field Theory" (pdf lecture notes)  by Uwe-Jens Wiese  (2007).
  • Quantum Field Theory  by Mark Srednicki  (Cambridge2007)pdf draft.
     
  • "A First Book on Quantum Field Theory"  by A. Lahiri& P.B. Pal (2005).
  • Quantum Field Theory in a Nutshell   by Anthony Zee  (Princeton,2003).
  • "A Modern Introduction to QFT"  by Michele Maggiore (Oxford).
  • "Field Quantization"  by Walter Greiner & Joachim Reinhardt (Springer).
  • An Introduction to QFT  Michael E. Peskin & Dan V. Schroeder(1995).
  • Quantum Field Theory   by Lewis H. Ryder  (Cambridge, 1985,1996).
  • "Quantum Field Theory"  by F. Mandl & G. Shaw (Wiley, 1984,1993).
  • "Field Theory: A Modern Primer"  by Pierre Ramond (1990).
  • "Advanced Quantum Mechanics"  by Jun John Sakurai (1967).
  • The Quantum Theory of Fields   by Steven Weinberg (Cambridge; Foundations (I)1995,Applications (II)1996,Supersymmetry (III)2000.

Videos :

 
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Quantum Field Theory


(2018-06-17)  
The key measurement which motivated renormalized  calculations.

  • Hans Bethe  understood physically that  .../...  Bethe was first to publish a rough result agreeing with experiment and assignedtwo of his graduate students the task of making more careful calculations:
    • Dick Scalettar for the relevant spin-½ electron  (he stalled).
    • Freeman Dyson  for an unphysical spin-0 particle. A training exercise handed to Dyson as his very first research problem.

 Come back later, we're still working on this one...


(2017-06-28)  

In 1947, Polykarp Busch  made a precise determination of themagnetic moment of the electron expressed in Bohr magnetons,  namely:

1.00119

 Come back later, we're still working on this one...

Julian Schwinger (1918-1994) was the first to make a fully-relativistictheoretical computation consistent with the experimental results,  giving centerstage to Green's function (it seems Schwinger was the first to promote that name).  Few people besides Schwinger's ownstudents took the time and effort to understand what he was really doing (with the notable exception of Freeman Dyson). Shortly thereafter, Richard Feynman also got the right answer with the help of his own newly-introduced Feynman diagrams, which made the subject far more accessible.  It was later revealed that Tomonaga  had reached thesame conclusions by himself in war-torn Japan. It is Freeman Dyson  who showed that the approachesof those three people were equivalent (thus Dyson was instrumental in the joint award of the1965 Nobel Prize  for that workto Tomonaga, Schwinger and Feynman).

Dyson  hinted that the theory could be carried to higher orders using perturbation theorybut he carefully stated that he reserved judgement concerning the ultimate convergence of the method. This was wise:  Although QED gives incredibly precise result at low orders (because the single dimensionless coupling constant of QED happens to be so small)  the method rapidly becomes intractable and ultimatelywas shown not to converge  at high orders.


(2007-07-23)  
Particles are modes of a quantized field.

 Come back later, we're still working on this one...


(2007-08-06)  

The following units are used, respectively, for spin, electric charge and mass.

Elementary Fermions  (matter) :

At first,  nobody knew why there should be three  generationsof fermions.  Ordinary matter is entirely made from fermionsof the first generation;  the elctron and two  (composite)  nucleons (a proton consists of two up-quarks and a down-quark, a neutronconsists of one up-quark and two down-quarks). When the muon  was first identified as a heavy version of the electron.I.I. Rabi (1898-1988) famously exclaimed:  "Who ordered that?"

Toshihide Maskawa (1940-)  and Makoto Kobayashi (1944-) split half of the 2008 Nobel Prize for finding "the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature". They did so in 1973,  when the existence of a third  generation hadn't yet been observed (thebottom quark was only discovered in1977,  by a Fermilab team led by Leon Lederman, 1922-2018). So far,  the existence of a fourth generation  hasn't been quite ruled out experimentally, but nearly so.

Each generation can be identified by its charged lepton, but this only commonlydone for neutrinos.  So, commonly talk of the electron neutrino or the muon antineutrino which arenot known by any other name. The use of ordinary numerals for generation numbers is occasionally encountered instead of traditional names or unnumbered abbreviations.

For quarks,  u1, d1, u2, d2, u3 and d3  stand for  u, d, c, s, t and b.

Leptons  (no color) Quarks  (colored)
NameSpinChargeMassNameSpinChargeMass
 e
 e
1/2
1/2
 -1 
 0 
 0.510998928(11) 
 < 0.01 
 u 
 d 
1/2
1/2
+2/3
-1/3
 2.2 
 4.7 
 
 
1/2
1/2
 -1 
 0 
 105.6583755(23) 
 < 0.2 
 c 
 s 
1/2
1/2
+2/3
-1/3
 1275(35) 
 92.4(25) 
 
 
1/2
1/2
 -1 
 0 
 1776.86(12) 
 < 20 
 t 
 b 
1/2
1/2
+2/3
-1/3
 17276(30) 
   4180(40) 

In addition to the classification in three generations, a practical distinctionis also made between light quarks  (u,d,s, generically q) and heavy quarks  (c,b,t, generically Q).  The elusive tetraquarks are generally thought to be:

qqQQ.

Quarks are normally not observed alone but in composite particles knownas hadrons  of which there are two broad types,mesons  and baryons :

  • meson  is a boson consisting of a quarkand its antiquark.
  • A  baryon  is a fermion combining 3 quarksin a color-neutral way.

Elementary Bosons  (force fields) :

Electroweak Bosons Other Elementary Bosons
NameSpinChargeMassNameSpinChargeMass
  
(photon)
 1  0  0 G
(graviton)
200
 Z0 1  0  91187 g
100
 W
 W +
 1 
 1 
 -1 
 +1 
 80370  H0
(Higgs boson)
00125350)

All interactions between fermions are mediated by at a boson, although that boson may beso short-lived that the thing may look like a contact interaction.

One of the electroweak vector bosons, the photon, is massless and described by a vector potential A, governed by Maxwell's equations. The other three are massive and are governed by Proca's equations, first formulated in 1936 (beforeYukawa  by Alexandru Proca  (1897-1955,Ph.D. 1933),a student of Louis de Boglie (1892-1987).


(2012-07-31)  
The whole hadron  zoo: Mesons  (2 quarks)  and baryons  (3 quarks).

Hadrons were defined as  strongly interacting particles  in 1962, by Lev Okun (1929-2015).

What sre listed below as components of hadrons are their valence quarks.

Some Mesons   (ordered by discovery date)
DateNameSymbolQuarksSpinChargeMassLifetime
1947charged
pions
ud
u
d
0+1
1
139.57021(14)26 ns
1950neutral
pions
0uu
dd
(uudd)/2
00 
 
134.97657(50)
 
 
84 as
1944
1947
charged
kaons
K+
K-
us
u
s
0+1
1
493.677(16)12.38(2) ns
1956neutral
kaons
K0
K0
 ds 
 sd 
00  
K0S
K0L
 (ds+sd) /2
 (dssd)/2 
497.611(13)8.954(4) ps
51.16(21) ns
1974psionJ/cc003096.9168zs
1977upsilonbb00946012.1zs

By analogy with the well-studied case of neutral kaons, it would seem that neutral pions are only observedin the superposition of up and down quark-antiquark pair stated third  (all others being probably too short lived or forbiden). I was unable to find a source confirming this.

The first charged kaon was spotted in 1944 at the laboratory of Polytechnique by Louis Leprince-Ringuet (1901-2000) who also coined the word hyperon  in 1953 to denote anybaryon with at least one strange  quark in combination with up or down quarks (only).

Some Baryons   (ordered by discovery date)
DateNameSymbolQuarksSpinChargeMassLifetime
1911protonpuud1/2+1938.272
1932neutronnudd1/20939.565881 s
 delta
resonances
 uuu 
 uud 
 udd 
 ddd 
3/2 +2 
 +1 
 0 
 -1 
12325.6 ys
1950lambda0uds1/201115.7263 ps
1953sigmauus1/2+1118980 ps
1959
1952
xi cascades-uss
dss
1/20
-1
1315
1322
290 ps
164 ps
1964omegaminussss3/2-1167282 ps
2007cascade Bbdsb1/2-157921.42 ps

It's often heard that "there are more than 200 distinct baryons". That statement is probably based on the fact that the 6 quarks and their 6 antiparticlesform 12 distinct particles.  There are 220 = C(12,3)  combinations of 3 of these,not accounting for possible mixing...

 Come back later, we're still working on this one...


(2007-07-12)  
A relativistic equation for bound-state problems.

This was first published in 1950,  without derivation,  at the endof a paper by Yoichiro Nambu (1921-2005).

 Come back later, we're still working on this one...


(2012-07-22)  
Richard P. Feynmann.

 Come back later, we're still working on this one...


(2012-07-22)  
Beyond Ward's identities...

The central idea behind renormalization is the fact that couplings depend on the scaleunder consideration  (in termes of either momentum or distance). Yet some relations stay the same.

FromCharles-Eugène Guye (1866-1942)toRichard P. Feynmann (1918-1988)andKenneth G. Wilson (1936-2013).

The renormalization group  was discovered in 1953 by two teams:

 Come back later, we're still working on this one...


(2019-01-15)  
Unitary matrix relating a final state of free particles to the initial state.

 Come back later, we're still working on this one...


(2019-03-23)  
Making quantum theory compatible with special relativity.

quantum field  is an operator-valued distributionover a spacetime whose dimension  d  is crucial.

 Come back later, we're still working on this one...


(2019-03-23)  
Greatest lower bound of the energies of states orthogonal to the vacuum.

 Come back later, we're still working on this one...


(2019-01-15)  
Greatest lower bound of the energies of states orthogonal to the vacuum.

 Come back later, we're still working on this one...


(2019-01-15)  

 Come back later, we're still working on this one...


(2023-02-28)  

 Come back later, we're still working on this one...


(2019-01-15)  

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(2016-06-18)  
As understood independently by several  different teams,  in 1964-65.

The experimental discovery of a Higgs-like particle was ceremoniously announced by CERNon  4 July 2012.

On 14 March 2013,  CERN confirmed that thenewly-discovered particle has zero spin and even parity  (two key property of the predicted Higgs boson) duly paving the way for the award of the 2013 Nobel prize to Higgs and Englert (which stirred up a controversy about the other aforementioned physicists who were left out).

Weak hypercharge .../...

 Come back later, we're still working on this one...


(2020-05-05)  
Tools intended for the old pion-mediated nuclear forcescan now be applied to Higgs interactions.

In simpler times,  it was thought that all nucear interactions couldbe mediated by a single spinless particle which was hastlily identified with thepion (pseudoscalar meson) recently discover by Hideki Yukawa. That got Yuakwa theNobel prize (1949). The mass of the neutral pion had roughly the correct mass to explain the short range of nuclear interactions.

 Come back later, we're still working on this one...


(2018-08-01)  

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