Ebook: New Developments in Quantum Field Theory

Quantum field theory is one of most central constructions in 20th century th- retical physics, and it continues to develop rapidly in many different directions. The aim of the workshop “New Developments in Quantum Field Theory”, which was held in Zakopane, Poland, June 14-20, 1997, was to capture a broad selection of the most recent advances in this field. The conference was sponsored by the Scientific and - vironmental Affairs Division of NATO, as part of the Advanced Research Workshop series. This book contains the proceedings of that meeting. Major topics covered at the workshop include quantized theories of gravity, string theory, conformal field theory, cosmology, field theory approaches to critical phenomena and the renormalization group, matrix models, and field theory techniques applied to the theory of turbulence. One common theme at the conference was the use of large-Nmatrix models to obtain exact results in a variety of different disciplines. For example, it has been known for several years that by taking a suitable double-scaling limit, certain string theories (or two-dimensional quantum gravity coupled to matter) can be re-obtained from the large-Nexpansion of matrix models. There continues to be a large activity in this area of research, which was well reflected by talks given at our workshop. Remarkably, large- Nmatrix models have very recently – just a few months before our meeting – been shown to have yet another deep relation to string theory.

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Lecturers: The Structure of 2D Quantum Space-Time; J. Ambj?rn. Scaling Laws in Turbulence; K. Gawedzki. Field Theory as Free Fall; A.Carlini, J. Greensite. Center Dominance, Center Vortices, and Confinement; L.D. Debbio, et al. Duality and the Renormalization Group; P.E. Haagensen. Unification of the General Nonlinear Sigma Model and the Virasoro Master Equation; J. de Boer, M. Halpern. A Matrix Model Solution of the Hirota Equation; V.A. Kazakov. Lattice Approximation of Quantum Electrodynamics; J. Kijowski, G. Rudolph.Seminar Speakers: Collective Dynamics of a Domain Wall; H. Arodz. Path Space Formulation of the BFV Theorem; K. Bering. Surplus Anomaly and Random Geoetries; P. Bialas, et al. Topological Contents of 3D Seiberg-Witten Theory; B. Broda. Free Strings in Noncritical Dimensions; M. Daszkiewicz, et al. Seiberg-Witten Theory, Integrable Systems and D-Branes; A. Marshakov. Microscopic Universality in random Matrix Models of QCD; S.M. Nishigaki. New Developments in Non-Hermitian Random Matrix Models; R.A. Janik, et al. 11 Additional Articles. Index.

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Lecturers: The Structure of 2D Quantum Space-Time; J. Ambj?rn. Scaling Laws in Turbulence; K. Gawedzki. Field Theory as Free Fall; A.Carlini, J. Greensite. Center Dominance, Center Vortices, and Confinement; L.D. Debbio, et al. Duality and the Renormalization Group; P.E. Haagensen. Unification of the General Nonlinear Sigma Model and the Virasoro Master Equation; J. de Boer, M. Halpern. A Matrix Model Solution of the Hirota Equation; V.A. Kazakov. Lattice Approximation of Quantum Electrodynamics; J. Kijowski, G. Rudolph.Seminar Speakers: Collective Dynamics of a Domain Wall; H. Arodz. Path Space Formulation of the BFV Theorem; K. Bering. Surplus Anomaly and Random Geoetries; P. Bialas, et al. Topological Contents of 3D Seiberg-Witten Theory; B. Broda. Free Strings in Noncritical Dimensions; M. Daszkiewicz, et al. Seiberg-Witten Theory, Integrable Systems and D-Branes; A. Marshakov. Microscopic Universality in random Matrix Models of QCD; S.M. Nishigaki. New Developments in Non-Hermitian Random Matrix Models; R.A. Janik, et al. 11 Additional Articles. Index.
Content:
Front Matter....Pages i-ix
The Structure of 2D Quantum Space-Time....Pages 1-21
Scaling Laws in Turbulence....Pages 23-31
Field Theory as Free Fall....Pages 33-45
Center Dominance, Center Vortices, and Confinement....Pages 47-64
Duality and the Renormalization Group....Pages 65-77
Unification of the General Non-Linear Sigma Model and the Virasoro Master Equation....Pages 79-95
A Matrix Model Solution of the Hirota Equation....Pages 97-112
Lattice Approximation of Quantum Electrodynamics....Pages 113-126
Three Introductory Talks on Matrix Models of Superstrings....Pages 127-146
New Developments in the Continuous Renormalization Group....Pages 147-158
Primordial Magnetic Fields and Their Development (Applied Field theory)....Pages 159-170
Towards Matrix Models of IIB Superstrings....Pages 171-178
Quantum Mechanics of the Electric Charge....Pages 179-185
Universal Fluctuations in Dirac Spectra....Pages 187-216
Determination of Critical Exponents and Equation of State by Field Theory Methods....Pages 217-232
Collective Dynamics of a Domain Wall — an Outline....Pages 233-241
Path Space Formulation of the BFV Theorem....Pages 243-249
Surplus Anomaly and Random Geometries....Pages 251-259
Topological Contents of 3D Seiberg-Witten Theory....Pages 261-268
Free Strings in Non-Critical Dimensions....Pages 269-277
Seiberg-Witten Theory, Integrable Systems and D-Branes....Pages 279-286
Microscopic Universality in Random Matrix Models of QCD....Pages 287-295
New Developments in Non-Hermitian Random Matrix Models....Pages 297-314
Potential Topography and Mass Generation....Pages 315-327
Past the Highest-Weight, and What You Can Find There....Pages 329-339
The Spectral Dimension on Branched Polymer Ensembles....Pages 341-348
Solving the Baxter Equation in High Energy QCD....Pages 349-357
Back Matter....Pages 359-364

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Lecturers: The Structure of 2D Quantum Space-Time; J. Ambj?rn. Scaling Laws in Turbulence; K. Gawedzki. Field Theory as Free Fall; A.Carlini, J. Greensite. Center Dominance, Center Vortices, and Confinement; L.D. Debbio, et al. Duality and the Renormalization Group; P.E. Haagensen. Unification of the General Nonlinear Sigma Model and the Virasoro Master Equation; J. de Boer, M. Halpern. A Matrix Model Solution of the Hirota Equation; V.A. Kazakov. Lattice Approximation of Quantum Electrodynamics; J. Kijowski, G. Rudolph.Seminar Speakers: Collective Dynamics of a Domain Wall; H. Arodz. Path Space Formulation of the BFV Theorem; K. Bering. Surplus Anomaly and Random Geoetries; P. Bialas, et al. Topological Contents of 3D Seiberg-Witten Theory; B. Broda. Free Strings in Noncritical Dimensions; M. Daszkiewicz, et al. Seiberg-Witten Theory, Integrable Systems and D-Branes; A. Marshakov. Microscopic Universality in random Matrix Models of QCD; S.M. Nishigaki. New Developments in Non-Hermitian Random Matrix Models; R.A. Janik, et al. 11 Additional Articles. Index.
Content:
Front Matter....Pages i-ix
The Structure of 2D Quantum Space-Time....Pages 1-21
Scaling Laws in Turbulence....Pages 23-31
Field Theory as Free Fall....Pages 33-45
Center Dominance, Center Vortices, and Confinement....Pages 47-64
Duality and the Renormalization Group....Pages 65-77
Unification of the General Non-Linear Sigma Model and the Virasoro Master Equation....Pages 79-95
A Matrix Model Solution of the Hirota Equation....Pages 97-112
Lattice Approximation of Quantum Electrodynamics....Pages 113-126
Three Introductory Talks on Matrix Models of Superstrings....Pages 127-146
New Developments in the Continuous Renormalization Group....Pages 147-158
Primordial Magnetic Fields and Their Development (Applied Field theory)....Pages 159-170
Towards Matrix Models of IIB Superstrings....Pages 171-178
Quantum Mechanics of the Electric Charge....Pages 179-185
Universal Fluctuations in Dirac Spectra....Pages 187-216
Determination of Critical Exponents and Equation of State by Field Theory Methods....Pages 217-232
Collective Dynamics of a Domain Wall — an Outline....Pages 233-241
Path Space Formulation of the BFV Theorem....Pages 243-249
Surplus Anomaly and Random Geometries....Pages 251-259
Topological Contents of 3D Seiberg-Witten Theory....Pages 261-268
Free Strings in Non-Critical Dimensions....Pages 269-277
Seiberg-Witten Theory, Integrable Systems and D-Branes....Pages 279-286
Microscopic Universality in Random Matrix Models of QCD....Pages 287-295
New Developments in Non-Hermitian Random Matrix Models....Pages 297-314
Potential Topography and Mass Generation....Pages 315-327
Past the Highest-Weight, and What You Can Find There....Pages 329-339
The Spectral Dimension on Branched Polymer Ensembles....Pages 341-348
Solving the Baxter Equation in High Energy QCD....Pages 349-357
Back Matter....Pages 359-364
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