A Few Papers by Arthur Jaffe in PDF file format. A Few Papers by Arthur Jaffe in PDF file format.
Research papers are above; expository papers are below. This list may be out of date.
For a complete list of publications, see the Full Publication List
RESEARCH PAPERS:
Entropic Central Limit Theorem and Quantum Inverse Subset Theorem arXiv:2401.14385
Magic Can Enhance the Quantum Capacity of Channels arXiv:2401.12105
Stabilizer Testing and Magic Entropy, (with Kaifeng Bu and Weichen Gu) arXiv:2306.09292
The Quantum Perron-Frobenius Space, (with Linzhe Huang, Zhengwei Liu, and Jinsong Wu) arXiv:2305.18971
Magic from a Convolutional Approach, (with Kaifeng Bu and Weichen Gu) arXiv:2302.08423
Entropy and Central Limit Theorem: A Convolutional Approach (with Kaifeng Bu and Weichen Gu) arXiv:2302.07841
Magic of Random Matrix Product States (with Liyuan Chen, Roy J. Garcia, and Kaifeng Bu) arXiv:2211.10350
Resource theory of quantum scrambling (with Roy Garcia and Kaifeng Bu) arXiv:2208.10477 to be published in PNAS
Wasserstein Complexity of Quantum Circuits (with Lu Li, Kaifeng Bu, Dax Enshan Koh, and Seth Lloyd) arXiv:2208.06306
Barren plateaus from learning scramblers with local cost functions (with Roy J. Garcia, Chen Zhao, and Kaifeng Bu) arXiv:2205.06679
Complexity of Quantum Circuits via Sensitivity, Magic and Coherence (with Kaifeng Bu, Roy J. Garcia, Dax Enshan Koh, and Lu Li) arXiv:2204.12051
Classical shadows with Pauli-invariant unitary ensembles (with Kaifeng Bu, Dax Enshan Koh, and Roy J. Garcia, arXiv:2202.03272
Quantifying scrambling in quantum neural networks (with Roy Garcia and Kaifeng Bu) arXiv:2112.01440
Quantum Scrambling with Classical Shadows (with Roy Garcia and You Zhou) arxiv:2102.01008
Quantum Fourier Analysis (with Chunlan Jiang, Zhengwei Liu, Yunxiang Ren, and Jinsong Wu) arxiv:2002.03477, PNAS 117:20 (2020), 10715-10720.
A Mathematical Picture Language Project (with Zhengwei Liu), arXiv:2006.03954, ICCM Proceedings, to appear
Reflection Positivity and Levin-Wen Models (with Zhengwei Liu) arXiv: , Expositones Mathematicae, to appear
Duaity of Graph Invariants (with Kaifeng Bu and Weichen Gu) arXiv:1810.08633 Science China Mathematics, to appear
de Finetti Theorems for Braided Parafermions (with Kaifeng Bu, Zhengwei Liu, and Jinsong Wu) arXiv: , Comm. Math. Phys., to appear
Reflection Positivity Then and Now Oberwolfach Reports
Mathematical Picture Language Program (with Zhengwei Liu) arXiv:1708.02604, PNAS
Quon 3D Language for Quantum Information (with Zhengwei Liu and Alex Wozniakowski) arXiv:1612.02630, PNAS
Constructive Simulation and Topological Design of Protocols (with Zhengwei Liu and Alex Wozniakowski) arXiv:1611.06447 New Journal of Physics
A New Diagrammatic Approach to Quantum Information (with Zhengwei Liu and Alex Wozniakowski) for QIP 2017
Reflection Positive Doubles (with Bas Janssens) arXiv:1607.07126, Journal of Functional Analysis
Multipartite Compressed Teleportation (with Zhengwei Liu and Alex Wozniakowski) arXiv:1605.00321
Holographic Software for Quantum Networks (with Zhengwei Liu and Alex Wozniakowski) arXiv:1605.00127 Science China Mathematics, to appear.
Qudit Isotopy (with Zhengwei Liu and Alex Wozniakowski) arXiv:1602.02671
Planar Para Algebras, Reflection Positivity (with Zhengwei Liu) arXiv:1602.02662 Communications in Mathematical Physics
Characterization of Reflection Positivity: Majoranas and Spins (with Bas Janssens) arXiv:1506.04197 Communications in Mathematical Physics
Stochastic PDE, Reflection Positivity, and Quantum Fields arXiv:1411.2964 Journal of Statistical Physics
Reflection Positivity for Parafermions (with Fabio L. Pedrocchi) arXiv:1406.1384 Communications in Mathematical Physics
Topological Order and Reflection Positivity (with Fabio L. Pedrocchi) arXiv:1310.5370 Europhysics Letters (EPL)
Reflection Positivity for Majoranas (with Fabio L. Pedrocchi) arXiv:1305.1792 Annals Henri Poincaré
Vortex Loops and Majoranas (with Stefano Chesi, Daniel Loss, and Fabio L. Pedrocchi) arXiv:1305.6270 Journal of Mathematical Physics cover article
Complex Classical Fields: A Framework for Reflection Positivity (with Christian Jaekel and Roberto E. Martinez II)
Compex Classical Fields and Partial Wick Rotation (with Christian Jäkel and Roberto E. Martinez II)
Quantization Domains (with Rajan Hoole and Christian Jäkel)
Earlier:
Replica Condensation and Tree Decay (with David Moser)
Reflection Positivity and Monotonicity (with Gordon Ritter), submitted for publication.
Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries (with Gordon Ritter), to appear in Comm. Math. Phys.
Quantum Field Theory on Curved Backgrounds. I. The Euclidean Functional Integral (with Gordon Ritter), published in Comm. Math. Phys. 270 (2007), 545—572.
An Exchange Identity for Non-Linear Fields (with Christian Jäkel), published in Comm. Math. Phys. 264 (2006), 283—289.
Quantum Yang-Mills Theory (with Edward Witten), published in The Millennium Prize Problems, American Mathematical Society 2006.
Derivatives with Twists, published in Reviews in Mathematical Physics, 14 (2002), 887—895.
The Elliptic Genus and Hidden Symmetry
Twist Fields, the Elliptic Genus, and Hidden Symmetry
Twist Fields and Broken Super-symmetry (with Olivier Grandjean), published in Journal of Mathematical Physics 41 (2000) 3698-3763.
Twist Positivity for Lagrangian Symmetries (with Olivier Grandjean and Jon Tyson)
Twist Positivity
The Holonomy Expansion, Index Theory, and Approximate Super-symmetry
Quantum Harmonic Analysis and Geometric Invariants, published in Advances in Mathematics 143 (1999) 1-110.
EXPOSITION and other PAPERS:
Bookplate Story Pdf File
Personal Interactions with my Dear Friend: Derek Robinson Pdf File
The Beginning and the Unifinished Story of the Millennium Prize Problems (with Boqing Xue), arXiv:2007.12473
Rudolf Haag, with Henning Rehren in Physics Today, July 2016
Multiple Reflections, Robert Schrader 23 May 2016, ETH Zurich (large file slow to download)
Raymond Stora and Les Houches 1970 arXiv:1604.08771 Nuclear Physics
Interview with Pauline Barrieu on Models and Uncertainty
Hirzebruch Lecture 2015, 13 October in the University Club, Bonn
CMP 50, An Essay about Communications in Mathematical Physics (This file is nearly 50 MB, so it takes a while to download.)
Life as a Mathematician, Talk at the Closing Ceremony of the 6th International Tournament of Young Mathematicians, Bremen, 18 July 2014 (Honorary Chairman of the Jury)
First Encounters, to appear in the Notices of the American Mathematical Society
Nine Lessons of my Teacher Arthur Strong Wightman. A Talk at Princeton University 10 March 2013, Published in the International Association of Mathematical Physics Newsletter, April 2013
Arthur Strong Wightman (with Barry Simon) published in the International Association of Mathematical Physics Newsletter, January 2013
Remembering Raoul Bott, published in the Notices of the American Mathematical Society Volume 60, pages 398--416 (2013)
The Glory of Three, published in the Program Book of the Kartause Ittingen Music Festival, 25--28 May 2012
James Glimm (with Thomas Spencer)
Scalar Bosons. Course Notes for Quantum Field Theory 253a, Fall 2007 (work in progress).
Quantum Theory and Relativity, Dedicated to George Mackey, to appear. This review focuses on the questions: Does physics suggest a way to combine quantum theory, relativity, and interaction?
To what extent can one formulate such quantum physics as mathematics? What is the present status of quantum field theory? What new mathematics emerges? What new insight does one apparently require to make further progress?
Constructive Jürg: A Personal Overview of Constructive Quantum Field Theory This is a talk given 3 July 2007 at the E.T.H. Zurich duirng the meeting entitled "The Inexhaustible Electron."
Lunch with George published in Notices of the American Mathematical Society, August 2007, Volume 54, pages 833-836.
BBC Interveiw on the Solution of the Poincaré Conjecture "The World Today," 16 August 2006 .
The Millennium Grand Challenge in Mathematics, published in Notices of the American Mathematical Society, June-July 2006, Volume 53, pages 652-660.
Witten Citation IAMP Meeting Rio, 9 August 2006.
Introduction to Quantum Field Theory, Spring 2005 Lecture Notes (work in progress).
Constructive Quantum Field Theory, published in Mathematical Physics 2000, pages 111-127, edited by A. Fokas, A. Grigoryan, T. Kibble, and B. Zegarlinski, Imperial College Press, London 2000
Reflections and Twists, written for the celebration of the 40th annivarsary of the IHES.
Roland L. Dobrushin (with J. Lebowitz and Ya. G. Sinai)
Theoretical Mathematics (with Frank Quinn)
Ordering the Universe: the Role of Mathematics, written for the David Report: Renewing U.S. Mathematics: Critical Resources for the Future, National Academy 1984. Reprinted in SIAM Review, in the Bulletin of the AMS, and in other places.
UNDERGRADUATE LECTURES:
Letures on Mechanics:
Lagrange Equations