Loops, Knots, Gauge Theories and Quantum Gravity

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Cambridge University Press, Jul 3, 2000 - Science - 321 pages
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Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. This text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. The book begins with a detailed review of loop representation theory. It then goes on to describe loop representations in Maxwell theory, Yang-Mills theories, as well as lattice techniques. The authors then discuss applications in quantum gravity in detail. Following chapters consider knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research.
  

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Contents

III
1
IV
3
V
7
VI
8
VII
10
VIII
17
IX
21
X
25
LXV
164
LXVI
168
LXVII
169
LXVIII
171
LXIX
172
LXX
173
LXXI
174
LXXII
175

XI
27
XII
29
XIII
30
XIV
32
XV
33
XVI
36
XVII
38
XIX
42
XX
44
XXI
47
XXII
50
XXIII
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XXIV
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XXV
56
XXVI
58
XXVII
61
XXVIII
63
XXIX
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XXX
67
XXXI
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XXXII
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XXXIII
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XXXIV
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XXXV
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XXXVI
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XXXVII
89
XXXVIII
92
XXXIX
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XL
103
XLII
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XLIII
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XLIV
112
XLV
113
XLVI
115
XLVII
118
XLIX
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L
124
LI
130
LII
131
LIII
133
LV
136
LVI
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LVII
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LVIII
144
LIX
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LX
147
LXI
150
LXII
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LXIII
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LXIV
161
LXXIII
179
LXXV
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LXXVI
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LXXVII
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LXXVIII
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LXXIX
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LXXX
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LXXXI
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LXXXIII
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LXXXIV
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LXXXV
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LXXXVI
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LXXXVII
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LXXXVIII
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XC
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XCI
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XCIV
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XCV
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XCVI
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XCVII
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XCVIII
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XCIX
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C
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CI
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CII
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CIII
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CIV
254
CV
260
CVI
264
CVIII
265
CIX
272
CX
274
CXI
275
CXII
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CXIII
280
CXIV
281
CXV
283
CXVI
285
CXVII
289
CXVIII
291
CXIX
292
CXX
294
CXXI
300
CXXII
302
CXXIII
304
CXXIV
309
CXXV
319
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