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Final Answers
© 2000-2023   Gérard P. Michon, Ph.D.

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 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.
Quantum Field 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  (Cambridge 2007) 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

Quantum Field theory was originally developped in Germany and Switzerland by the likes of Pauli, Heisenberg and Wigner...  Two main textbooks were published which Freeman Dyson read just before coming to America  (as he was taking courses given by  Nicholas Kemmer):


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

  • Hans Bethe  understood physically that   .../...   Bethe was first to publish a rough result agreeing with experiment and assigned two 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...

Willis Lamb (1913-2008; Nobel 1955)
Electromagnetic Radiation in Metallic Wave Guides  by  Richard Scalettar  (UW-Madison, 1943).
A New Postulational Foundation of Quantum Mechanics (162 pp.)  by  Richard Scalettar  (Cornell, 1959).
 
The Lamb shift:  Feynman, Schwinger & Weisskopf (3:53)  by  Hans Bethe   (Web of Stories, 2017-06-26).
The Lamb shift  (5:44 | 3:01)  by  Freeman Dyson  (Web of Stories, 1997).
When theory was in disgrace (1:57)  by  Murray Gell-Mann  (Web of Stories, 1998).
The race to calculate the relativistic Lamb shift (2:52)  Murray Gell-Mann  (Web of Stories, 1998).


(2017-06-28)   Quantum Electrodynamics   (QED)

In 1947,  Polykarp Busch  made a precise determination of the magnetic 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-relativistic theoretical computation consistent with the experimental results,  giving center stage to  Green's function  (it seems Schwinger was the first to promote that name).  Few people besides Schwinger's own students 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 the same conclusions by himself in war-torn Japan.  It is  Freeman Dyson  who showed that the approaches of those three people were equivalent  (thus Dyson was instrumental in the joint award of the 1965 Nobel Prize  for that work to Tomonaga, Schwinger and Feynman).

Understanding Schwinger (4:55)   by  Freeman Dyson  (Web of stories, 1997).
Equating the approaches of Feynman, Schwinger and Tomanaga (6:47)   by  Freeman Dyson  (1997).

Dyson  hinted that the theory could be carried to higher orders using perturbation theory but 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 ultimately was shown not to  converge  at high orders.

Polykarp Kusch (1911-1993; Nobel 1955).
Proca action   |   Alexandru Proca (1897-1955)
Stueckelberg action (1938)   |   Ernst Stueckelberg (1905-1984)
Propagator   |   Richard Feynman (1918-1988)
Abdus Salam (1926-1996)   |   John Ward (1924-2000)
 
Quantum foam (9:57)  by  Don Lincoln   (Fermilab, 2014-10-24).
Feynman diagrams (5:51)  by  Don Lincoln   (Fermilab, 2016-02-22).
Perturbation theory (8:31)  by  Don Lincoln   (Fermilab, 2016-03-24).
Quantum electrodynamics: theory (7:21)  by  Don Lincoln   (Fermilab, 2016-03-30).
QED: Experimental evidence (5:44)  by  Don Lincoln   (Fermilab, 2016-04-19).
The physics of g-2 (7:07)  by  Don Lincoln   (Fermilab, 2016-05-04).
 
Quantum Electrodynamics (15:21)  by  Matt O'Dowd   (PBS Space Time, 2017-06-28).
Solving the Impossible in QFT (15:20)  by  Matt O'Dowd   (PBS Space Time, 2017-07-12).
Quantum Theory's Most Incredible Prediction (16:29)  by  Matt O'Dowd   (PBS Space Time, 2018-08-15).


 Pascual Jordan
Pascual Jordan
1902-1980
(2007-07-23)   Second Quantization
Particles are modes of a  quantized field.

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

Scalar field theory   |   Canonical quantization
Quantum Field Theory (5:29)  by  Don Lincoln   (Fermilab, 2016-01-14).
Quantum Fields:  The Real Building Blocks of the Universe (1:00:17)  David Tong  (RI, 2017-02-15).


(2007-08-06)   Elementary Particles

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

Elementary Fermions  (matter) :

At first,  nobody knew why there should be  three  generations of fermions.  Ordinary matter is entirely made from fermions of the first generation;  the elctron and two  (composite)  nucleons  (a proton consists of two up-quarks and a down-quark, a neutron consists 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  (the bottom quark was only discovered in 1977,  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 commonly done for neutrinos.  So, commonly talk of the electron neutrino or the muon antineutrino which are not 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.

  • The  electron  (e-)  was discovered by  Jean Perrin  in 1895 and by  J.J. Thomson  in 1897.  The  positron  (e+)  is the antiparticle of the electron.  It was discovered in 1932 by  Carl Anderson (1905-1991).
  • The  muon  (m-)  was discovered in 1936 by  Anderson  and his very first doctoral student,  Seth Neddermeyer (1907-1988).
  • The  tauon  (t-)  was discovered in 1975 by Martin Perl (1927-2014).

Leptons  (no color)  Quarks  (colored)
NameSpinChargeMass NameSpinChargeMass
 e -
 ne
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 
 m -
 nm
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) 
 t -
 nt
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 distinction is 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 known as  hadrons  of which there are two broad types, mesons  and  baryons :

  • meson  is a boson consisting of a quark and its antiquark.
  • A  baryon  is a fermion combining 3 quarks in a color-neutral way.

Elementary Bosons  (force fields) :

Electroweak Bosons  Other Elementary Bosons
NameSpinChargeMass NameSpinChargeMass
 g 
(photon)
 1   0   0  G
(graviton)
2 0 0
 Z0  1   0   91187  g
(8 colored gluons)
1 0 0
 W -
 W +
 1 
 1 
 -1 
 +1 
 80370   H0
(Higgs boson)
0 0 125350 (150))

All interactions between fermions are mediated by at a boson, although that boson may be so 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 (before Yukawa  by  Alexandru Proca  (1897-1955, Ph.D. 1933), a student of  Louis de Boglie (1892-1987).

The Inevitability of Physical Laws: Why the Higgs Has to Exist  by  Nima Arkani-Hamed  (IAS, 2012-10-26).
The Salam Lecture Series 2012,  by  Nima Arkani-Hamed   1 | 2 | 3? | 4 | 5 |
 
Higgs Boson 2016 (7:52)  by  Don Lincoln   (Fermilab, 2016-11-16).
Broad categories of subatomic particles (9:48)  by  Don Lincoln   (Fermilab, 2018-08-29).


(2012-07-31)   Composite Hadrons Bound by the Strong Force  (QCD)
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
1947 charged
pions
p+
p-
ud
u
d
0 +1
-1
139.57021(14) 26 ns
1950 neutral
pions
p0 uu
dd
(uu-dd) /Ö2
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)  /Ö2
 (ds-sd) /Ö2 
497.611(13)8.954(4) ps
51.16(21) ns
1974psionJ/y cc 003096.9168 zs
1977upsilonU bb 00946012.1 zs

By analogy with the well-studied case of neutral kaons, it would seem that neutral pions are only observed in 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 any baryon with at least one  strange  quark in combination with up or down quarks (only).

Some Baryons   (ordered by discovery date)
DateNameSymbolQuarksSpinChargeMassLifetime
1911protonpuud 1/2+1 938.272 ¥
1932 neutronnudd 1/20 939.565 881 s
  delta
resonances
D++
D+
D0
D-
 uuu 
 uud 
 udd 
 ddd 
3/2  +2 
 +1 
 0 
 -1 
1232 5.6 ys
1950lambda L0uds 1/20 1115.7 263 ps
1953sigmaS+uus 1/2+1 1189 80 ps
1959
1952
xi cascades X0
X
-
uss
dss
1/20
-1
1315
1322
290 ps
164 ps
1964omega minusW-sss 3/2-1 1672 82 ps
2007cascade BXb-dsb 1/2-1 5792 1.42 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 antiparticles form 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...

1962 International Conference in Geneva (5:28)  by  Murray Gell-Mann  (1998).
 
99 Years of Discovery: What are Cosmic Rays?   by Nahee Park  (2011)
Wikipedia :   Quantum Chromodynamics   |   Timeline of particle discoveries
 
List of particles   |   List of baryons   |   List of mesons


(2007-07-12)   The Bethe-Salpeter Equation   (1951)
A relativistic equation for bound-state problems.

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

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

Bethe-Salpeter equation   |   Hans Bethe (1906-2005)   |   Edwin Salpeter (1924-2008)


(2012-07-22)   Path Integral Formulation   (Feynman, 1948)
Richard P. Feynmann.

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

Path integral formulation
 
Feynman's Infinite Quantum Paths (15:48)  by  Matt O'Dowd  (PBS Space Time, 2017-07-07)
Euclidean time & field theory (1:20:50)  #1  (PI, 2013-2014)
Operators & correlation functions (1:28:09)  #2  (PI, 2013-2014)
Killing vectors, Connections,Curvature, Cartan's Equations of Structure (1:03:51)  #3  (PI, 2013-2014)


(2012-07-22)   The Road to the Renormalization Group.
Beyond Ward's identities...

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

From Charles-Eugène Guye (1866-1942) to Richard P. Feynmann (1918-1988) and Kenneth G. Wilson (1936-2013).

The  renormalization group  was discovered in 1953 by two teams:

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

Ward-Takahashi identity   |   John Ward (1924-2000)   |   Yasushi Takahashi (1924-2013)
 
Landau pole   |   Quantum triviality   |   Renormalization   |   Divergent Series Redux
 
1951 precovery of the Chilean representation (3:48)  by  Murray Gell-Mann  (1998).
Oldstone conference: Renormalizability of theories (3:48)  by  Freeman Dyson  (Web of Stories, 1997).
1953-54:  Renormalization group by Gell-Mann & Francis Low:  1:20, 1:16.


(2019-01-15)   S-Matrix   (scaterring matrix)  in a scaterring process.
Unitary matrix relating a final state of free particles to the initial state.

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 still working on this one...

S-matrix   |   S-matrix theory (deprecated)


(2019-03-23)   Constructive Quantum Field Theory
Making  quantum theory  compatible with  special relativity.

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

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 still working on this one...

Constructive quantum field theory   |   Algebraic quantum field theory (AQFT)
Israel Gelfand (1913-2009)   |   Ed Nelson (1932-2014)


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

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 still working on this one...

Wightman axioms   |   Lars Gårding (1919-2014)   |   Arthur Wightman (1922-2013)


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

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 still working on this one...

Mass gap
Yang-Mills existence and mass gap:  One of the  unsolved  Millenium problems.


(2019-01-15)   Coleman-Mandula theorem  (1967)

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 still working on this one...

Coleman-Mandula theorem (1967)   |   Sidney Coleman (1937-2007)   |   Jeffrey Mandula (1941-)
Coleman-Mandula theorem aand Mandelstam variables (Physics Stack Exchange, 2011-01-23)


(2023-02-28)   Asymptotic freedom in QCD   (Gross, Wilczek and Politzer, 1973)

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 still working on this one...

David Gross (1941-)   |   Frank Wilczek (1941-)   |   David Politzer (1949-)


(2019-01-15)   Haag-Lopuszanski-Sohnius theorem  (1975)

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 still working on this one...

All Possible Generators Of Supersymmetries Of The S Matrix (Nuclear Physics B88 (1975) pp. 257-274)
Rudolf Haag (1922-2016)   |   Jan T. Lopuszanski (1923-2008)   |   Martin Sohnius
 
Haag-Lopuszanski-Sohnius theorem (1975)  in  nLab


(2016-06-18)   The  Higgs mechanism  gives a particle an intrinsic mass.
As understood independently by  several  different teams,  in 1964-65.

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

It was obvious to everybody that this was worth a Nobel prize.  A few months later,  the Nobel committee decided to wait a little and awarded instead a share of the 2012 prize to  my former coachSerge Haroche  for research unrelated to high-energy physics...  The media was  unprepared for this.

On 14 March 2013,  CERN confirmed that the newly-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...

Higgs mechanism   |   Nobel 2013  (Higgs & Englert)
The origins of the Brout-Englert-Higgs mechanism
 
The Higgs Mechanism (9:31)  by  Matt O'Dowd  (PBS Space Time, 2015-12-16)
 
Some math behind the Higgs Boson (2:51)  by  Brian Greene  (WSF, 2013-10-08)
 
Demystifying the Higgs Boson (1:15:05)  by  Leonard Susskind  (Stanford, 2012-08-06)

 Hideki Yukawa
Hideki Yukawa (1951)
 

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

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

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 still working on this one...

Yukawa inreraction   |   Hideki Yukawa (1907-1981; Nobel 1949)


(2018-08-01)   Production modes and decay channels of Higgs boson.

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 still working on this one...

Higgs boson   (CERN,  2012-07-04).
Higgs results at Moriond conference  by  Achintya Rao  (2018-03-19).
 
Demystifying the Higgs Boson (1:15:07)  by  Leonard Susskind  (2012-07-30)
Boson de Higgs et structure fine de l'espace temps (1:29:20)  by  Alain Connes  (Institut Fourier, 2014)

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 (c) Copyright 2000-2023, Gerard P. Michon, Ph.D.