Combinatorics of gauge fields

't Hooft, Gerard; Veltman, M.J.G.

doi:10.1016/S0550-3213(72)80021-X

Combinatorics of gauge fields

Gerard 't Hooft
(
- Utrecht U.
)
,
M.J.G. Veltman
(
- Utrecht U.
)

Jul, 1972

36 pages

Published in:

Nucl.Phys.B 50 (1972) 318-353

Published: 1972

DOI:

10.1016/S0550-3213(72)80021-X

View in:

OSTI Information Bridge Server

reference search650 citations

Citations per year

Abstract: (Elsevier)

Gauge field theories can be described by many different sets of Feynman rules, depending on the particular gauge chosen. In this paper a prescription for obtaining the Feynman rules in different gauges is given. A rigorous combinatorial proof of the independence of the S -matrix of the chosen gauge is presented. The proof is general and applies to Yang-Mills type theories as well as to gravitation. For renormalizable Yang-Mills type theories it is shown that the renormalized theory is invariant with respect to renormalized gauge transformations.

Note:

*** Nobel Prize <a href=http://www.nobel.se/announcement-99/physics99.html>1999</a> ***

References(22)

Figures(0)

Conservation of Isotopic Spin and Isotopic Gauge Invariance

Chen-Ning Yang
(
- Brookhaven
)
,
Robert L. Mills
(
- Brookhaven
)

- Phys.Rev. 96 (1954) 191-195,
- Also in *Lai, C. H. (Ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 29-33, and in *Yang, C.N.: Selected Papers 1945-1980*, 172-176,
•
DOI:
- 10.1103/PhysRev.96.191

Renormalization of Massless Yang-Mills Fields

Gerard 't Hooft
(
- Utrecht U.
)

- Nucl.Phys.B 33 (1971) 173-199,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 273-299
•
DOI:
- 10.1016/0550-3213(71)90395-6

Broken symmetries, massless particles and gauge fields

Peter W. Higgs
(
- Edinburgh U.
)

- Phys.Lett. 12 (1964) 132-133,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 125-126
•
DOI:
- 10.1016/0031-9163(64)91136-9

Broken Symmetries and the Masses of Gauge Bosons

Peter W. Higgs
(
- Edinburgh U.
)

- Phys.Rev.Lett. 13 (1964) 508-509,
- Also in *Lichtenberg, D. B. (Ed.), Rosen, S. P. (Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 155-156,
•
DOI:
- 10.1103/PhysRevLett.13.508

Spontaneous Symmetry Breakdown without Massless Bosons

Peter W. Higgs
(
- North Carolina U.
)

- Phys.Rev. 145 (1966) 1156-1163,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 133-140
•
DOI:
- 10.1103/PhysRev.145.1156

Broken Symmetry and the Mass of Gauge Vector Mesons

F. Englert
(
- Brussels U.
)
,
R. Brout
(
- Brussels U.
)

- Phys.Rev.Lett. 13 (1964) 321-323,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 127-129,
•
DOI:
- 10.1103/PhysRevLett.13.321

Global Conservation Laws and Massless Particles

G.S. Guralnik
(
- Imperial Coll., London
)
,
C.R. Hagen
(
- Imperial Coll., London
)
,
T.W.B. Kibble
(
- Imperial Coll., London
)

- Phys.Rev.Lett. 13 (1964) 585-587,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 130-132,
•
DOI:
- 10.1103/PhysRevLett.13.585

- Phys.Rev. 155 627

Renormalizable Lagrangians for Massive Yang-Mills Fields

Gerard 't Hooft
(
- Utrecht U.
)

- Nucl.Phys.B 35 (1971) 167-188,
- Also in *Lichtenberg, D. B. ( Ed.), Rosen, S. P. ( Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 171-192, and in *Lai, C.H. (ed.) Gauge Theory of Weak and Electromagnetic Interactions*, 300-321,
•
DOI:
- 10.1016/0550-3213(71)90139-8

Renormalizable massive vector meson theory. Perturbation theory of the Higgs phenomenon

Benjamin W. Lee
(
- Fermilab and
- SUNY, Stony Brook
)

- Phys.Rev.D 5 (1972) 823-835
•
DOI:
- 10.1103/PhysRevD.5.823

Spontaneously Broken Gauge Symmetries Part 1: Preliminaries

B.W. Lee
(
- Fermilab and
- SUNY, Stony Brook
)
,
Jean Zinn-Justin
(
- Fermilab and
- SUNY, Stony Brook
)

- Phys.Rev.D 5 (1972) 3121-3137,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 347-363
•
DOI:
- 10.1103/PhysRevD.5.3121

Spontaneously Broken Gauge Symmetries Part 2: Perturbation Theory and Renormalization

B.W. Lee
(
- Fermilab and
- SUNY, Stony Brook
)
,
Jean Zinn-Justin
(
- SUNY, Stony Brook
)

- Phys.Rev.D 5 (1972) 3137-3155,
- Phys.Rev.D 8 (1973) 4654 (erratum)
•
DOI:
- 10.1103/PhysRevD.5.3137

Spontaneously Broken Gauge Symmetries Part 3: Equivalence

B.W. Lee
(
- Fermilab
)
,
Jean Zinn-Justin
(
- SUNY, Stony Brook
)

- Phys.Rev.D 5 (1972) 3155-3160,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 381-386
•
DOI:
- 10.1103/PhysRevD.5.3155

Physical Processes in a Convergent Theory of the Weak and Electromagnetic Interactions

Steven Weinberg
(
- MIT, LNS
)

- Phys.Rev.Lett. 27 (1971) 1688-1691,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 199-202 and in *Rosner, J. L. ( Ed.): New Particles*, 40-43
•
DOI:
- 10.1103/PhysRevLett.27.1688

Feynman Diagrams for the Yang-Mills Field

- Phys.Lett.B 25 (1967) 29-30,
- ,
•
DOI:
- 10.1016/0370-2693(67)90067-6

Effect of anomalies on quasirenormalizable theories

David J. Gross
(
- Princeton U.
)
,
R. Jackiw
(
- MIT, LNS
)

- Phys.Rev.D 6 (1972) 477-493
•
DOI:
- 10.1103/PhysRevD.6.477

An Anomaly Free Version of Weinberg's Model

- Phys.Lett.B 38 (1972) 519-523,
- In *Rosner, J.L., (ed.): New Particles*, 44-48
•
DOI:
- 10.1016/0370-2693(72)90532-1

Regularization and Renormalization of Gauge Fields

Gerard 't Hooft
(
- Utrecht U.
)
,
M.J.G. Veltman
(
- Utrecht U.
)

- Nucl.Phys.B 44 (1972) 189-213,
- Also in *Lai, C. H. ( Ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 322-346
•
DOI:
- 10.1016/0550-3213(72)90279-9

Renormalization, diagrams, and gauge invariance

I. Bialynicki-Birula
(
- Pittsburgh U. and
- Warsaw U.
)

- Phys.Rev.D 2 (1970) 2877-2886
•
DOI:
- 10.1103/PhysRevD.2.2877

Generalized ward identities and yang-mills fields

M.J.G. Veltman
(
- CERN and
- Utrecht U.
)

- Nucl.Phys.B 21 (1970) 288-302
•
DOI:
- 10.1016/0550-3213(70)90521-3

Renormalization of a unified theory of weak and electromagnetic interactions

D.A. Ross
(
- Oxford U.
)
,
J.C. Taylor
(
- Oxford U.
)

- Nucl.Phys.B 51 (1973) 125-144,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 395-415,
- Nucl.Phys.B 58 (1973) 643-643 (erratum)
•
DOI:
- 10.1016/0550-3213(73)90505-1

Quantization and gauge freedom in a theory with spontaneously broken symmetry

York-Peng Yao
(
- Michigan U.
)

- Phys.Rev.D 7 (1973) 1647-1660
•
DOI:
- 10.1103/PhysRevD.7.1647