Project C - Understand the Yang-Mills problem. Reading List

Here's the first version of the reading list, the references in the official statement of the problem, in the order in which they are referred to in the text:

  • L. O’Raifeartaigh, The Dawning of Gauge Theory, Princeton University Press, 1997.
  • C. N. Yang and R. L. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. 96 (1954), 191–195.
  • S. Weinberg, A model of leptons, Phys. Rev. Lett. 19 (1967), 1264–1266.
  • A. Salam, Weak and electromagnetic interactions, in Svartholm: Elementary Particle Theory, Proceedings of The Nobel Symposium held in 1968 at Lerum, Sweden, Stockholm, 1968, 366–377.
  • D. J. Gross and F. Wilczek, Ultraviolet behavior of non-abelian gauge theories, Phys. Rev. Lett. 30 (1973), 1343–1346.
  • H. D. Politzer, Reliable perturbative results for strong interactions? Phys. Rev. Lett. 30 (1973), 1346–1349.
  • M. Creutz, Monte carlo study of quantized \(SU(2)\) gauge theory, Phys. Rev. D21 (1980), 2308–2315.
  • K. G. Wilson, Quarks and strings on a lattice, in New Phenomena In Subnuclear Physics, Proceedings of the 1975 Erice School, A. Zichichi, ed., Plenum Press, New York, 1977.
  • C. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw-Hill, New York, 1980.
  • R. Streater and A. Wightman, PCT, Spin and Statistics and all That, W. A. Benjamin, New York, 1964.
  • R. Haag, Local Quantum Physics, Springer Verlag, 1992.
  • K. Symanzik, Euclidean quantum field theory, in Local Quantum Theory, R. Jost, ed., Academic Press, New York, 1969, 152–226.
  • E. Nelson, Quantum fields and Markoff fields, in Proc. Sympos. Pure Math. XXIII 1971, AMS, Providence, R.I., 1973, 413–420.
  • K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s functions, Comm. Math. Phys. 31 (1973), 83–112, and Comm. Math. Phys. 42 (1975), 281–305
  • J. Fröhlich, K. Osterwalder, and E. Seiler, On virtual representations of symmetric spaces and theory analytic continuation, Ann. Math. 118 (1983), 461–489.
  • C. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw-Hill, New York, 1980
  • K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s functions, Comm. Math. Phys. 31 (1973), 83–112, and Comm. Math. Phys. 42 (1975), 281–305.
  • E. Witten, Supersymmetric Yang–Mills theory on a four-manifold, J. Math. Phys. 35 (1994), 5101–5135.
  • J. Glimm and A. Jaffe, Quantum Physics, Second Edition, Springer Verlag, 1987, and Selected Papers, Volumes I and II, Birkhäuser Boston, 1985.
  • A. Jaffe, Constructive quantum field theory, in Mathematical Physics, T. Kibble, ed., World Scientific, Singapore, 2000.
  • J. Glimm and A. Jaffe, The \( \lambda \phi_2^4 \) quantum field theory without cut-offs, I. Phys. Rev. 176 (1968), 1945–1951, II. Ann. Math. 91 (1970), 362–401, III. Acta. Math. 125 (1970), 203–267, and IV. J. Math. Phys. 13 (1972), 1568–1584.
  • J. Glimm, A. Jaffe, and T. Spencer, The Wightman axioms and particle structure in the \(P(\phi)_2\) quantum field model, Ann. Math. 100 (1974), 585–632.
  • F. Guerra, L. Rosen, and B. Simon, The \(P(\phi)_2\) Euclidean quantum field theory as classical statistical mechanics, Ann. Math. 101 (1975), 111–259
  • K. Osterwalder and R. S´en´eor, A nontrivial scattering matrix for weakly coupled \(P (\phi)_2\) models, Helv. Phys. Acta 49 (1976), 525–535
  • J. Fröhlich, On the triviality of \( \lambda \phi_d^4 \) theories and the approach to the critical point, Nucl. Phys. 200 (1982), 281–296.
  • M. Aizenman, Geometric analysis of \(\phi^4\) fields and Ising models, Comm. Math. Phys. 86 (1982), 1–48
  • J. Glimm, A. Jaffe, and T. Spencer, A convergent expansion about mean field theory, I. Ann. Phys. 101 (1976), 610–630, and II. Ann. Phys. 101 (1976), 631–669.
  • F. Guerra, L. Rosen, and B. Simon, Correlation inequalities and the mass gap in \( P(\phi)_2 \), III. Mass gap for a class of strongly coupled theories with non-zero external field, Comm. Math. Phys. 41 (1975), 19–32
  • J. Glimm and A. Jaffe, \( \phi^4_2 \) quantum field model in the single phase region: differentiability of the mass and bounds on critical exponents, Phys. Rev. 10 (1974), 536–539.
  • O. McBryan and J. Rosen, Existence of the critical point in \(\phi^4\) field theory, Comm. Math. Phys. 51 (1976), 97–105.
  • J. Imbrie, Phase diagrams and cluster expansions for low temperature P(ϕ)2 models, Comm. Math. Phys. 82 (1981), 261–304 and 305–343.
  • E. Seiler, Schwinger functions for the Yukawa model in two dimensions, Comm. Math. Phys. 42 (1975), 163–182.
  • D. Brydges, J. Fr¨ohlich, and E. Seiler, On the construction of quantized gauge fields, I. Ann. Phys. 121 (1979), 227–284, II. Comm. Math. Phys. 71 (1980), 159–205, and III. Comm. Math. Phys. 79 (1981), 353–399.
  • T. Balaban, D. Brydges, J. Imbrie, and A. Jaffe, The mass gap for Higgs models on a unit lattice, Ann. Physics 158 (1984), 281–319.
  • J. Magnen and R. S´en´eor, Yukawa quantum field theory in three dimensions, in Third International Conference on Collective Phenomena, J. Lebowitz et. al. eds., New York Academy of Sciences, 1980.
  • K. Gawedzki, Renormalization of a non-renormalizable quantum field theory, Nucl. Phys. B262 (1985), 33–48.
  • L. D. Faddeev and V. N. Popov, Feynman diagrams for the Yang–Mills fields, Phys. Lett. B25 (1967), 29–30.
  • C. Becchi, A. Rouet, and R. Stora, Renormalization of gauge theories, Ann. Phys. 98 (1976), 287–321
  • K. G. Wilson, Quarks and strings on a lattice, in New Phenomena In Subnuclear Physics, Proceedings of the 1975 Erice School, A. Zichichi, ed., Plenum Press, New York, 1977
  • K. Osterwalder and E. Seiler, Gauge theories on the lattice, Ann. Phys. 110 (1978), 440–471.
  • T. Balaban, Ultraviolet stability of three-dimensional lattice pure gauge field theories, Comm. Math. Phys. 102 (1985), 255–275
  • T. Balaban, Renormalization group approach to lattice gauge field theories. I: generation of effective actions in a small field approximation and a coupling constant renormalization in 4D, Comm. Math. Phys. 109 (1987), 249–301.
  • V. Rivasseau, From Perturbative to Constructive Renormalization, Princeton Univ. Press, Princeton, NJ, 1991.
  • J. Magnen, Vincent Rivasseau, and Roland S´en´eor, Construction of Y M4 with an infrared cutoff, Comm. Math. Phys. 155 (1993), 325–383
  • D. Brydges and P. Federbush, Debye screening, Comm. Math. Phys. 73 (1980), 197–246.
  • R. Feynman, The quantitative behavior of Yang–Mills theory in 2+1 dimensions, Nucl. Phys. B188 (1981), 479–512.
  • I. M. Singer, The geometry of the orbit space for nonabelian gauge theories, Phys. Scripta 24 (1981), 817–820.
  • B. Simon, Some quantum operators with discrete spectrum but classically continuous spectrum, Ann. Phys. 146 (1983), 209–220.
  • G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B72 (1974), 461–473.
  • N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang–Mills theory. Nucl. Phys. B426 (1994), 19–52.

Second Level

  • H. Minkowski. Phys. Zeitschr. 10 (1909) 104
  • C. Lanczos. Einstein and the Cosmic World Order. Wiley, New York, 1965.
  • V. Vizgen. Unified Field Theories in the First Third of the Twentieth Century.
  • D. Bailin. Weak Interactions. Hilger, Bristol, 1982.
  • C. Lai. Gauge Theory of the Weak and Electromagnetic Interactions. World Scientific, Singapore, 1981.
  • P. Becher, P. Bohm and H. Joos. Gauge Theories of the Strong and Electroweak Interactions. Wiley, New York, 1984.
  • M. Peshkin and A. Tonomura. The Aharonov-Bohm Effect. Lecture Notes in Physics 340, Springer-Verlag 1989.
  • C. Ehresmann. Colloque de Topologie. Brussels 1950.
  • S. Kobayashi and K. Nomizu. Foundations of Differential Geometry. Interscience, 1969.
  • L. Okun. Proc. JINR-CERN School of Physics, CERN, Geneva 1983.
  • C. Jarlskog. In Physica Scripta 24 No. 5 (1981) 867.
  • A. Koestler. The Sleepwalkers. Grosset and Dunlap, New York 1963.
  • T. T. Wu and C. N. Yang, Phys. Rev. D12 (1975) 3845.
  • T.-P. Chen and L.-F. Li. Gauge Theory of Elementary Particle Physics. Clarendon Press, Oxford (1984).

Starting to read The Dawning of Gauge Theory, I hit a wall at this sentence:

"Let the electric and magnetic fields \( \vec{E} \) and \( \vec{B} \) be written as a single antisymmetric Lorentz tensor \( F_{\mu \nu} \), where \( F_{oi} = E_i \) and \( F_{ij} = \epsilon_{ijk} B_k \).

Making a note: I cannot make further progress until I know what a Lorentz tensor is.

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