**Stephen Louis Adler** (born November 30, 1939) is an American physicist specializing in elementary particles and field theory.

## Biography

Adler was born in New York City. He received an A.B. degree at Harvard University in 1961, where he was a Putnam Fellow, and a Ph.D. from Princeton University in 1964. He is the son of Irving Adler and Ruth Adler and older brother of Peggy Adler.

Adler was elected a Fellow of the American Academy of Arts and Sciences in 1974.^{[1]} He became a member of the Institute for Advanced Study in 1966, becoming a full Professor of Theoretical Physics in 1969, and was named "New Jersey Albert Einstein Professor" at the institute in 1979.

He has won the J. J. Sakurai Prize from the American Physical Society in 1988, and the Dirac Medal of the International Centre for Theoretical Physics in 1998, among other awards.

Adler's seminal papers on high energy neutrino processes, current algebras, soft pion theorems, sum rules, and perturbation theory anomalies helped lay the foundations for the current standard model of elementary particle physics.

In 2012, Adler contributed to a family venture when he wrote the foreword for his then 99-year-old father's 87th book, "Solving the Riddle of Phyllotaxis: Why the Fibonacci Numbers and the Golden Ratio Occur on Plants". The book's diagrams are by his sister Peggy.^{[2]}

## Trace dynamics

In his book *Quantum Theory as an Emergent Phenomenon*, published 2004, Adler presented his trace dynamics, a framework in which quantum field theory emerges from a matrix theory. In this matrix theory, particles are represented by non-commuting matrices, and the matrix elements of bosonic and fermionic particles are ordinary complex numbers and non-commuting Grassmann numbers, respectively. Using the action principle, a Lagrangian can be constructed from the trace of a polynomial function of these matrices, leading to Hamiltonian equations of motion. The construction of a statistical mechanics of these matrix models leads, so Adler says, to an “emergent effective complex quantum field theory”.^{[3]}^{[4]}

Adler's Trace Dynamics has been discussed in relation to the differential space theory of quantum systems by Norbert Wiener and Amand Siegel, to its variant by David Bohm and Jeffrey Bub, and to modifications of the Schrödinger equation by additional terms such as the quantum potential term or stochastic terms, and to hidden variable theories.^{[5]}

## Publications

- Books

- Stephen L. Adler:
*Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory*, Cambridge University Press, 2004, ISBN 978-0-521-11597-1, 978-0-521-83194-9 - Stephen L. Adler:
*Adventures in Theoretical Physics: Selected Papers of Stephen Adler with Commentaries: Selected Papers with Commentaries*, World Scientific Series in 20th Century Physics, World Scientific Publishing Co., 2006, ISBN 978-9-812-56370-5 - Stephen L. Adler:
*The Guide to PAMIR, Theory and Use of Parameterized Adaptive Multidimensional Integration Routines*, World Scientific Publishing Co., 2012, ISBN 978-981-4425-03-2 - Stephen L. Adler:
*Quaternionic Quantum Mechanics and Quantum Fields*, International Series of Monographs on Physics, Oxford University Press, 1994, ISBN 978-0-195-06643-2

## References

**^**"Book of Members, 1780-2010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 6 April 2011.**^**Adler, Irving.*Solving the Riddle of Phyllotaxis: Why the Fibonacci Numbers and the Golden Ratio Occur On Plants*. Retrieved 8 June 2012.**^***Quantum Theory as an Emergent Phenomenon*: Book review by Collin Carbno**^**See also the review of Adler's trace dynamics in Tejinder P. Singh:*The connection between ‘emergence of time from quantum gravity’ and ‘dynamical collapse of the wave-function in quantum mechanics’*, International Journal of Modern Physics D, vol. 19, no. 14 (2010), pp. 2265–2269, World Scientific Publishing Company, DOI 10.1142/S0218271810018335 (full text). Preprint: arXiv:1005.2682v2 (submitted on 15 May 2010, version of 12 October 2010)**^**Mark Davidson:*Stochastic mechanics, trace dynamics, and differential space – a synthesis*, arXiv:quant-ph/0602211, submitted 25 February 2006, version of 21 Mar 2006