** A Few Papers by Arthur Jaffe in PDF file format.**

Research papers are above; expository papers are below.

**RESEARCH PAPERS****:**

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:**

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