His book "Quantum Field Theory" (1994) has been well received. Pierre Ramond's review in Science states that Brown's book is "marked by its astute choice of topics as well as by the clarity with which they are expounded, it is akin to a toolbox for students of modern quantum field theory... a very thorough and rare treatment...a very interesting and original textbook. I strongly recommend this book to whoever aspires to become either a particle or a condensed matter physicist."[6]
Brown's work on the interaction of intense laser beams with electrons (Brown & Kibble 1964) is still cited forty or so years later.
Brown was the first to compute the stress–energy tensor between conducting planes (Brown & Maclay 1969). The stress tensor evaluated on a plane yields the Casimir force.
Brown was the first to exhibit the classical limit of the hydrogen atom (1973).[7]
He constructed large-quantum-number wave packets that slowly spread while moving in circular orbits.
At the University of Washington, Hans Dehmelt captured single charged particles in very stable orbits in a Penning trap. This arrangement, called geonium, enabled measurement of the magnetic moment of the electron with exquisite precision for which Dehmelt won the Nobel Prize. Brown became fascinated with this new experimental procedure and with coworkers wrote many papers investigating the detailed workings of geonium. His work culminated in a long review article (Brown & Gabrielse 1986) that has become a handbook for other experimenters who use a Penning trap.
Brown also investigated plasma effects on nuclear fusion (Brown & Sawyer 1997), wrote a paper applying field theory to plasma physics (Brown & Yaffe 2001), obtained the non-leading corrections in plasma stopping power (Brown et al. 2005), and provided an effective field description for deuterium-tritium fusion (Brown & Hale 2014).
Brown, L. S.; Cassidy, J. P. (1977). "Stress-tensor trace anomaly in a gravitational metric: General theory, Maxwell field". Physical Review D. 15 (10): 2810. Bibcode:1977PhRvD..15.2810B. doi:10.1103/physrevd.15.2810.
Basham, C. L.; Brown, L. S.; Ellis, S. D.; Love, S. T. (1979). "Energy correlations in electron–positron annihilation in quantum chromodynamics: Asymptotically free perturbation theory". Physical Review D. 19 (7): 2018. Bibcode:1979PhRvD..19.2018B. doi:10.1103/physrevd.19.2018. S2CID121310426.
Brown served on many committees of the American Physical Society and was the first academic Editor of Physical Review D.
During his tenure (1987-1995), he was instrumental in incorporating author-prepared electronic manuscripts into the journal's editorial and publishing process, and he conceived and promoted an early version of the electronic status inquiry system for authors.[8]
Additional activities:
Los Alamos National Laboratory: Consultant (1974-2001); Theoretical Division External Advisory Committee, Member (1990-1993)
U.S. D.O.E. Technical Assessment Committee on University Programs, Chairman, Theoretical Physics Panel (1982-1983)