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Scholarly Interest Report
Paul M. Stevenson
Professor Emeritus
Professor Emeritus of Physics and Astronomy
  • B.A. Natural Sciences (1976) Cambridge University, Cambridge, England
  • Ph.D. Theoretical Physics (1979) Imperial College, London, England
Primary Department
   Department of Physics and Astronomy
Department Affiliations
  • Department of Physics and Astronomy
    Research Areas
     Quantum Field Theory, Elementary Particle Physics
    Research in Quantum Field theory

    My research is in theoretical particle physics and quantum field theory. Field theory combines quantum theory and relativity and provides the framework for the fundamental theories of particle physics.

     I have a longstanding interest in optimizing renormalized perturbation theory in Quantum Chromodynamics (QCD) and other theories.  Conventional perturbation theory yields ambiguous results dependent on the arbitrary renormalization scheme choice.  The "Principle of Minimal Sensitivity" approach developed in my 1981 paper resolves this issue and has some deep implications.  When higher-order calculations became available in the early '90's Mattingly and I showed that optimized perturbation theory, without any extra ad-hoc inputs, predicts "freezing" behaviour at low energies, in accord with many phenomenological indications.  I have recently been exploring the mathematical properties of the optimization equations in high orders with the aim of substantiating my conjecture that optimization provides an "induced convergence" mechanism, even though perturbation series in any fixed renormalization scheme are factorially divergent. 

     Another central theme of my work relates to the nature of the vacuum  -- or, in more technical terms, with the dynamics of the scalar field responsible for the spontaneous symmetry breaking that drives the Higgs Mechanism of the Standard Model.

    In the Standard Model the vacuum is not empty but is filled with a background scalar field. In work with M. Consoli I have shown that this background field can be viewed as a background density of particles. These particles (dubbed 'phions') are nearly massless, spinless particles that interact via a point-like repulsive interaction and a long-range attractive (-1/r3) potential (arising as a relativistic, quantum effect from the fundamental repulsive point-like interaction). Despite the rest-energy ('E=mc2') cost of each particle, the long-range attraction makes it energetically favourable to fill space with a specific density of phions. Thus, the vacuum (the lowest-energy state) is not empty but is filled with a spontaneously generated Bose-Einstein condensate of phions. The elementary excitations of this condensate are not phions (which are thus unobservable) but much heavier 'quasiparticles,' corresponding to the yet-to-be-discovered Higgs particles.

    This picture implies that the vacuum is a sort of medium. As such, one would expect its very long-wavelength excitations to be describable by hydrodynamics. I have explored some consequences of this simple but powerful idea. For a normal medium the hydrodynamic equations always have an acoustic regime where sufficiently weak disturbances obey the linear wave equation with a characteristic propagation speed, the speed of sound. However, a vacuum medium has no such linear regime; disturbances are always nonlinear, no matter how weak. The empty-vacuum and Higgs-vacuum cases are very different; they correspond to the speed of sound becoming zero or infinite, respectively. A cloud of cold atoms can be viewed as a disturbance of the empty vacuum and its free expansion, when the trapping potential is turned off, is correctly described by the empty-vacuum hydrodynamic equations. The corresponding equations in the Higgs-vacuum case are much stranger -- they have a similar form but with the roles of space and time interchanged.

    Teaching Areas
     Graduate: Quantum Field Theory, Classical Dynamics.
    Undergraduate: Classical Mechanics, Quantum Mechanics.
    Selected Publications
     Refereed articles

    P. M. Stevenson, Optimization of QCD perturbation theory: Results for Re+e- at fourth order, Nucl. Phys. B 868 (2013) 38-64.


    P.M. Stevenson, Fixed and unfixed points: Infrared limits in optimized QCD perturbation theory, Nucl. Phys. B 875 (2013) 63-79


    P. M. Stevenson "The long-range interaction in massless (lambda Phi^4)_4 theory." Modern Physics letters A, 24: 261-271.


    P. M. Stevenson, "Hydrodynamics of the Vacuum." Intl. J. Mod. Phys. A, 21: 2877-2903.


    P. M. Stevenson "Comparison of perturbative RG theory with lattice data for the 4d Ising model." Nuclear Physics B, 729 (2005) : 542-557.


    P. M. Stevenson "How do sound waves in a Bose-Einstein condensate move so fast?." Physical Review A, 68 (2003) : 055601-1-3.


    M. Consoli and P. M. Stevenson "Physical mechanisms generating spontaneous symmetry breaking and a hierarchy of scales." International Journal of Modern Physics, A15 (2000) : 133-157.


    P. Cea, M. Consoli, L. Cosmai, and P.M. Stevenson "Further lattice evidence for a large re-scaling of the Higgs condensate." Modern Physics Letters, A14 (1999) : 1673-1686.

     Conference papers

    P. M. Stevenson "Are there pressure waves in the vacuum?." Proceedings of the Second Meeting on CPT and Lorentz Symmetry (2001) : 346-350.


    "The vacuum as a medium." University of Houston, Clear Lake, Clear Lake, TX. (1/25/2007)


    ""Impossible" probabilities and quantum reality,." Families Weekend, Rice University. (9/15/2006)


    "Hydrodynamics of the vacuum." University of Pittsburgh, Pittsburgh, PA. (Jan. 6th, 2005)


    "Hydrodynamics of the vacuum." University of Bari, Bari, Italy. (June 22nd, 2005)


    "Monte-Carlo data for the 4d Ising model: Does it fit the conventional Renormalization-Group description?." University of Catania, Catania, Italy. (June 16th, 2005)

     Seminar Speaker

    Seminar at University of Catania, Italy


    "The long-range interaction in massless lambda phi^4 theory and its RG description." University of Catania, Catania, Italy. (June 2007)

     The vacuum as a medium, PHENO 2002, University of Wisconsin-Madison, April 2002
    Supervised Theses & Dissertations
     Syed Asif Hassan, M.S. Effective potential calculation for a nonlocal scalar field theory. (2006) (Thesis or Dissertation Director)

    Awards, Prizes, & Fellowships
     George R. Brown Award for Superior teaching, Rice University (May 2012)