Home page of Daniel Friedan

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Teaching

Fall 2012: General Physics 204

Research

I work on two projects: one concerning the fundamental laws of physics, the other concerning certain condensed matter systems that might eventually be useful in quantum computers. Both projects use the technology of two-dimensional quantum field theory.

I have formulated and am investigating a physical mechanism that at least formally determines the background spacetime for string theory. The hope is that this mechanism will actually produce the combination of General Relativity and the Standard Model of particle physics that has so accurately described physics across an astonishingly wide range of distance scales.

My efforts in this direction started with my doctoral thesis, first presented in a talk at the 1979 Nuffield Workshop on Quantum Gravity, then published as a letter, Physical Review Letters 45 (1980) 1057, then published in full as LBL Report LBL-11517 (1980) and reprinted as Annals of Physics 163 (1985) 318.  Other early work was presented in 1982 lectures at Les Houches, and in 1984 lectures at Aspen and at the Santa Fe APS Meeting.

The theory I am currently working on was presented in a paper in 2002:  A tentative theory of large distance physics.  A summary was presented at Cargese 2002. A short sketch was given at the 2003 Wigner Symposium (transparencies).

The most recent steps were mathematical explorations of the Yang-Mills flow, presented in a paper: A loop of SU(2) gauge fields stable under the Yang-Mills flow (2010).

I am also trying to understand the basic properties of near-critical quantum circuits. These are one-dimensional condensed matter systems near a low temperature critical point. I have argued that such systems are the only physical systems that are practical for asymptotically large-scale quantum computers.

These systems behave in universal ways which are described by 1+1 dimensional quantum field theories. Universal physical properties of these systems can be discovered by investigating the general structures of 1+1 dimensional quantum field theories.

My first efforts in this direction were my doctoral thesis (see above) and Physical Review Letters 52 (1984) 1575, and Physics Letters B151 (1985) 37.

More papers in this area:

• On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature (2003)
• Entropy flow in near-critical quantum circuits (2005)
• Entropy flow through near-critical quantum junctions (2005)
• Infrared properties of boundaries in one-dimensional quantum systems (2005)
• Supersymmetric 1+1D boundary field theory (2008)
• General properties of the boundary renormalization group flow for supersymmetric systems in 1+1 dimensions (2008)
• Gradient formula for the beta function of 2D quantum field theory (2009)

Papers

• Publications listed in the SPIRES Database

Unpublished manuscripts:

• Geometric Models for Critical Systems in 2+&epsilon Dimensions, 1979 manuscript, prepared for the directors of the Nuffield Workshop on Quantum Gravity.
• The Space of Conformal Boundary Conditions for the c=1 Gaussian model, 1999 note, circulated privately.
• The Space of Conformal Boundary Conditions for the c=1 Gaussian model (more), 2003 note, circulated privately.

Copies of some older papers:

• Nonlinear Models in 2+&epsilon Dimensions, Physical Review Letters 45 (1980) 1057.
• Nonlinear Models in 2+&epsilon Dimensions, U.C. Berkeley doctoral thesis, LBL Report LBL-11517 (1980) (scanned)
• Nonlinear Models in 2+&epsilon Dimensions, U.C. Berkeley doctoral thesis reprinted as Annals of Physics 163 (1985) 318.
• Some Nonabelian Toy Models in the Large N Limit, Communications in Mathematical Physics 78 (1981) 353-362.
• A Proof of the Nielsen-Ninomiya Theorem, Communications in Mathematical Physics 85 (1982) 481-490.
• Introduction to Polyakov's String Theory, Les Houches lectures (1982) (scanned).
• Conformal Invariance, Unitarity and Two Dimensional Critical Exponents, published in Vertex Operators in Mathematics and Physics -- Proceedings of a Conference November 10-17, 1983, Publications of the Mathematical Sciences Research Institute #3, Springer-Verlag (1984) (scanned).
• Supersymmetric Derivation of the Atiyah-Singer Index and the Chiral Anomaly, Nuclear Physics B235 (1984) 395.
• Covariant Methods in Superstring Theory, preprint EFI-85-09 (scanned), published in Proceedings of the Annual Meeting of the APS Division of Particles and Fields, Santa Fe, Oct 31 - Nov 3, 1984, p. 437.
• Conformal Invariance, Unitarity, and Critical Exponents in Two Dimensions, Physical Review Letters 52 (1984) 1575.
• Superconformal Invariance in Two Dimensions and the Tricritical Ising Model, Physics Letters B151 (1985) 37.
• Random walks in two-dimensional random random environments with constrained drift forces, Physical Review A31, 6 (1985) 3841-3845.
• Notes on String Theory and Two Dimensional Conformal Field Theory, preprint EFI-85-99 (scanned), published in the Proceedings of the Workshop on Unified String Theories, Santa Barbara, July 29 - August 16, 1985, p. 162.
• Strings in Background Fields, Nuclear Physics B262 (1985) 593.
• Covariant Quantization of Superstrings, Physics Letters B160 (1985) 55.
• On Two-Dimensional Conformal Invariance And The Field Theory Of String, Physics Letters B162 (1985) 102.
• Conformal invariance, supersymmetry and string theory, Nuclear Physics B271 (1986) 93.
• String field theory, Nuclear Physics B271 (1986) 540.
• All free string theories are theories of forms, Nuclear Physics B274 (1986) 71.
• Covariant quantization of supersymmetric string theories: The spinor field of the Ramond-Neveu-Schwarz model, Nuclear Physics B278 (1986) 577.
• Details of the Non-Unitarity Proof for Highest Weight Representations of the Virasoro Algebra, Communications in Mathematical Physics 107 (1986) 535-542.
• Determinant Formulae and Unitarity for the N=2 Superconformal Algebras in Two-Dimensions or Exact Results on String Compactification, Physics Letters B172 (1986) 316.
• The integrable analytic geometry of quantum string, Physics Letters B175 (1986) 287.
• The Analytic Geometry of Two Dimensional Conformal Field Theory, Nuclear Physics B281 (1987) 509.
• A New Formulation of String Theory, Physica Scripta T15 (1987) 78-88.
• The Conformal Field Theory of Orbifolds, Nuclear Physics B282 (1987) 13.
• Super Characters and Chiral Asymmetry in Superconformal Field Theory, Nuclear Physics B296 (1988) 779.
• Phenomenology and Conformal Field Theory or Can String Theory Predict the Weak Mixing Angle, Nuclear Physics B299 (1988) 613.
• c-Theorem and Spectral Representation, Nuclear Physics B352 (1991) 616.

Copies of more recent papers:

• A tentative theory of large distance physics, JHEP 0310:063 (2003).
• Boundary Entropy of One-dimensional Quantum Systems at Low Temperature, Physical Review Letters 93 (2004) 030402.
• Entropy flow in near-critical quantum circuits, arXiv:cond-mat/0505084.
• Entropy flow through near-critical quantum junctions, arXiv:cond-mat/0505085.
• Infrared properties of boundaries in one-dimensional quantum systems, Journal of Statistical Mechanics P03014 (2006).
• Supersymmetric 1+1D boundary field theory, Journal of Physics A: Mathematical and Theoretical 42 (2009) 304015.
• General properties of the boundary renormalization group flow for supersymmetric systems in 1+1 dimensions, Advances in Theoretical and Mathematical Physics 13 no. 6 (2009) 0810.0611.
• Gradient formula for the beta function of 2D quantum field theory, Journal of Physics A: Mathematical and Theoretical 43 (2010) 215401.
• A loop of SU(2) gauge fields stable under the Yang-Mills flow, Surveys in Differential Geometry, Vol. 15 (2010), Perspectives in mathematics and physics: Essays dedicated to Isadore Singer's 85th birthday, edited by Tomasz Mrowka and Shing-Tung Yau, Publisher: International Press of Boston.

Talks:

• Cargese 2002 transparencies
• Wigner Symposium 2003 transparencies
  
• Talks on rg flows, the Ricci flow, and the Yang-Mills flow:
  • Introduction to the Renormalization Group Flow (Banff, April 15, 2008)
  • A conjecture on the Ricci flow (Banff, April 16, 2008)
  • Supersymmetric 1+1d boundary field theory (Conference in Memory of Alexei Zamolodchikov, Moscow, June 22, 2008)
    
  • Properties of the boundary renormalization group flow (Strasbourg, September 12, 2008)
  • Quantum field theory and the Ricci flow (Reykjavik, October 20, 2008)
  • Gradient property of the boundary rg flow for supersymmetric 1+1d quantum field theories (Munich, November 24, 2008)
  • Introduction to the 2d Nonlinear Model and the Renormalization Group Flow (Stony Brook, January 22, 2009)
  • Gradient property of the boundary rg flow for supersymmetric 1+1d quantum field theories (Edinburgh, January 28, 2009)
  • Preliminary evidence for a stable 2-sphere in the Yang-Mills flow for SU(3) gauge fields on S4 (Pisa, June 24, 2009)
  • Pisa talk: Addendum July 6, 2009
  • A loop of SU(2) gauge fields on S^4 stable under the Yang-Mills flow (MIT, November 3, 2009)

Links to other people's work

• Cosmic View: The Universe in 40 Jumps   by Kees Boeke
       (a book for children published in 1957)
  

Other links

• physics webmail
• Rutgers webmail
• Notebook

Revised August 26, 2010