Dr Martin Lavelle

Biography

Role

I am the Associate Head of the School of Engineering, Computing and Mathematics with responsibility for Admissions and Outreach. If you would like to find out more about our degrees, please get in touch with me.

I have a strong interest in outreach and regularly talk in schools and at public events, including recently at a local science fiction convention. Please contact me if you would like to arrange a talk.

My research is in theoretical physics and I currently teach calculus, vector calculus and supervise mathematics project students. I also teach mechanics to engineering students.

Teaching

Teaching interests

I am a University Teaching Fellow and a Fellow of the Higher Education Academy. In Plymouth I have taught at all levels including on our mathematics degrees, service teaching and year zero. I have also taught abroad, including undergraduate lectures in Germany and Ireland, postgraduate lectures in Spain and an invited course of postgraduate lectures in Canada.

I have a long held interest in using technology to help students improve their understanding of mathematics and science.

I have an interest in creating screen capture videos to help support student learning. Many of these are available through our YouTube collection. Most of my work here is focused on calculus.

The results of some older work on creating interactive pdf files are freely available here plymouth.ac.uk/mathaid. as 50 pdf files with exercises and quizzes on topics ranging from elementary algebra to proof by induction. This work was funded by various LTSN and FDTL grants.

Students have more than once nominated me for a Student Union award for inspirational teaching. I have also twice been nominated for outstanding support.

Research

Research interests

My research is in quantum field theory and I am a member of the Plymouth Particle Theory Group. I have worked at universities in several countries and visited/spoken at many institutions including CERN, Japan's KEK, and the Thomas Jefferson National Acceleration Facility.

I am especially interested in constructing locally gauge invariant descriptions of charged states and in the infra-red structure of gauge theories. This is intimately related to why quarks and gluons are confined. A key physical idea here is that charges are intimately connected to the background field that they generate.

The Nobel Prize for Physics was awarded in 2018 for ideas that have led to modern ultra-high power lasers. Such devices provide extremely intense background fields and my most recent papers are focused on how strong field Quantum Electrodynamics (QED) describes electrons in high intensity laser backgrounds. For example, the electron acquires a mass shift which we have recently shown is independent of the polarisation inside the full elliptic class of polarisations.

Copies of my publications may be found here. An earlier review of some of the central ideas is here.

Publications

Key publications are highlighted

Journals
Articles
Lavelle M & McMullan D 2019 'One loop Volkov propagator in the Lorentz class of gauges' Physics Letters B 798, 135021-135021 , DOI
Lavelle M & McMullan D 2019 'Renormalization of the Volkov propagator' Physical Review D 100, (3) , DOI PEARL
Lavelle M & McMullan D 2018 'Electrons in an eccentric background field' Physical Review D 97, (3) , DOI PEARL
Lavelle M & McMullan D 2015 'Fermionic propagator in an intense background' Physical Review D 91, (10) , DOI
Lavelle M & McMullan D 2014 'Sideband mixing in intense laser backgrounds' Physics Letters B 739, 421-424 , DOI
Lavelle M, McMullan D & Raddadi M 2013 'Propagation in an intense background' PHYSICAL REVIEW D 87, (8) Author Site , DOI
Lavelle MJ, McMullan D & Sharma P 2012 'Factorization of glue and mass terms in SU(N) gauge theories' Physical Review D 85, (4) Publisher Site , DOI
Lavelle M, McMullan D & Steele T 2012 'Soft Collinear Degeneracies in an Asymptotically Free Theory' Advances in High Energy Physics 2012, 1-10 , DOI
Ilderton A, Lavelle M & McMullan D 2010 'Symmetry breaking, conformal geometry and gauge invariance' JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL 43, (31) Author Site , DOI PEARL
Ilderton A, Lavelle M & McMullan D 2010 'Stability, creation and annihilation of charges in gauge theories' ANNALS OF PHYSICS 325, (4) 835-851 Author Site , DOI PEARL
Ilderton A, Lavelle M & McMullan D 2009 'Physical charges in QED and QCD' Proceedings of Science PEARL
Langfeld K, Heinzl T, Ilderton A, Lavelle M & McMullan D 2008 'Solution of the Gribov problem from gauge invariance' PoS Confinement 8, 047-047 Author Site PEARL
Heinzl T, Ilderton A, Langfeld K, Lavelle M & McMullan D 2008 'Ice-limit of Coulomb gauge Yang-Mills theory' Physical Review D 78, (7) Author Site Publisher Site , DOI PEARL
Heinzl T, Ilderton A, Langfeld K, Lavelle M, Lutz W & McMullan D 2008 'Is the ground state of Yang-Mills theory Coulombic?' Physical Review D 78, (3) , DOI PEARL
Heinzl T, Ilderton A, Langfeld K, Lavelle MJ, Lutz W & McMullan D 2008 'Is the ground state of Yang-Mills theory Coulombic?' Physical Review D 78, (3) Publisher Site , DOI
Heinzl T, Ilderton A, Langfeld K, Lavelle M, Lutz W & McMullan D 2008 'Probing the ground state in gauge theories' Physical Review D 77, (5) , DOI PEARL
Heinzl T, Ilderton A, Langfeld K, Lavelle MJ, Lutz W & McMullan D 2008 'Probing the ground state in gauge theories' Physical Review D 77, (5) , DOI
McMullan D 2007 'Charges in Gauge Theories' Symmetry, Integrability and Geometry: Methods and Applications , DOI
Ilderton A, Lavelle M & McMullan D 2007 'Colour, copies and confinement' Journal of High Energy Physics 2007, (3) PEARL
Heinzl T, Langfeld K, Lavelle M & McMullan D 2007 'Coulomb gauge Gribov copies and the confining potential' Physical Review D 76, (11)
Lavelle M & McMullan D 2007 'Initial states: IR and collinear divergences' Nuclear Physics B-Proceedings Supplements 174, 51-54
Gerdt V, Horan R, Khvedelidze A, Lavelle M, McMullan D & Palii Y 2006 'On the Hamiltonian reduction of geodesic motion on SU(3) to SU(3)/SU(2)' Journal of Mathematical Physics 47 (11), , DOI
Lavelle M & McMullan D 2006 'Collinearity, convergence and cancelling infrared divergences' Journal of High Energy Physics 2006, (03) 026-026 , DOI
Bagan E, Lavelle M & McMullan D 2006 'Anti-screening by quarks and the structure of the inter-quark potential' Physics Letters B 632, (5-6) 652-656
Lavelle M & McMullan D 2006 'Collinearity, convergence and cancelling infrared divergences' Journal of High Energy Physics 2006, (3)
Lavelle M & Mazumder Z 2004 'Infra-red finite, physical electron propagator in 2+1 dimensions' Physics Letters B 596, (1-2) 70-76
Bagan E, Horan R, Kovner A, Lavelle M, Mazumder Z, McMullan D & Tanimura S 2004 'On electric and magnetic charges in gauge theories' Nuclear Physics B-Proceedings Supplements 133, 277-280
Kovner A, Lavelle MJ & McMullan D 2002 'On nonexistence of magnetic charge in pure Yang-Mills theories' Journal of High Energy Physics 6, (12) 939-948
Kovner A, Lavelle MJ & McMullan D 2002 'On Nonexistence of Magnetic Charge in Pure Yang-Mills Theories' Journal of High Energy Physics 2002 (12), , DOI PEARL
Bagan E, Lavelle M, McMullan D & Tanimura S 2002 'Structure of screening in QED' Physical Review D 65, (10)
Horan R, Lavelle M & McMullan D 2000 'Asymptotic dynamics in quantum field theory' Journal of Mathematical Physics 41, (7) 4437-4451 , DOI
Bagan E, Lavelle M & McMullan D 2000 'Charges from Dressed Matter: Construction' Annals of Physics 282, (2) 471-502 , DOI
Bagan E, Lavelle M & McMullan D 2000 'Charges from Dressed Matter: Physics and Renormalisation' Annals of Physics 282, (2) 503-540 , DOI
Bagan E, Lavelle M & McMullan D 2000 'Electrons and photons: fact not fiction' Physics Letters B 477, (1-3) 396-400 , DOI
Bagan E, Lavelle M & McMullan D 2000 'The structure of the QCD potential in 2+1 dimensions' Physics Letters B 477, (1-3) 355-360 , DOI
Lavelle M & McMullan D 1999 'Hadrons without strings' Physics Letters B 471, (1) 65-71 , DOI
Lavelle M & McMullan D 1998 'Colour charges and the anti-screening contribution to the interquark potential' Physics Letters B 436, (3-4) 339-343 , DOI
Bagan E, Lavelle M & McMullan D 1998 'Soft dynamics and gauge theories' Physical Review D 57, (8) R4521-R4524 , DOI
Bagan E, Lavelle M & McMullan D 1997 'Infrared finite electron propagator' Physical Review D 56, (6) 3732-3743 , DOI
Bagan E, Fiol B, Lavelle M & McMullan D 1997 'Infrared Finite Charge Propagation' Modern Physics Letters A 12, (25) 1815-1821 , DOI
Lavelle M & McMullan D 1997 'Constituent quarks from QCD' Physics Reports 279, (1) 1-65 , DOI
Lavelle M & McMullan D 1996 'The colour of quarks' Physics Letters B 371, (1-2) 83-86 , DOI
Bagan E, Lavelle M & McMullan D 1996 'The physical propagator of a slowly moving charge' Physics Letters B 370, (1-2) 128-134 , DOI
Lavelle M & McMullan D 1995 'Lavelle and McMullan Reply' Physical Review Letters 75, (22) 4151-4151 , DOI
Lavelle M & McMullan D 1995 'Observables and gauge fixing in spontaneously broken gauge theories' Physics Letters B 347, (1-2) 89-94 , DOI
Breckenridge JC, Lavelle MJ & Steele TG 1995 'The Nielsen identities for the two-point functions of QED and QCD' Zeitschrift für Physik C Particles and Fields 65, (1) 155-164 , DOI
Lavelle MJ, Nasrallah NF & Schilcher K 1994 'The pion polarisability from QCD sum rules' Physics Letters B 335, (2) 211-214 , DOI
LAVELLE MJ & MCMULLAN D 1994 'NONLOCAL SYMMETRY FOR QED - REPLY' PHYSICAL REVIEW LETTERS 73, (7) 1048-1048 Author Site , DOI
Lavelle M & McMullan D 1994 'Perturbative and non-perturbative quarks and gluons' Physics Letters B 329, (1) 68-74 , DOI
Lavelle M & McMullan D 1993 'Nonlocal symmetry for QED' Physical Review Letters 71, (23) 3758-3761 , DOI
Lavelle M & McMullan D 1993 'Gauge choices and physical variables in QED' Physics Letters B 316, (1) 172-174 , DOI
Lavelle M & McMullan D 1993 'On the physical propagators of QED' Physics Letters B 312, (1-2) 211-214 , DOI
Lavelle M & McMullan D 1993 'The radiation class: a set of temporal gauges' Zeitschrift für Physik C Particles and Fields 59, (2) 351-356 , DOI
Kahana D & Lavelle M 1993 'On the Pauli-Villars regularisation scheme in the NJL model' Physics Letters B 298, (3-4) 397-399 , DOI
Lavelle MJ & Oleszczuk M 1992 'Gauge-dependent condensates and the quark propagator' Physics Letters B 275, (1-2) 133-136 , DOI
Kahana D & Lavelle M 1992 'Non-local condensates in the Nambu model' Physics Letters B 275, (1-2) 129-132 , DOI
Ahlbach J, Lavelle M, Schaden M & Streibl A 1992 'Propagators and four dimensional condensates in pure QCD' Physics Letters B 275, (1-2) 124-128 , DOI
Lavelle M & Oleszczuk M 1991 '$$\left\langle {:\bar \psi \psi :} \right\rangle$$ and three-point functions in QCD' Zeitschrift für Physik C Particles and Fields 51, (4) 615-618 , DOI
Lavelle M 1991 'Gauge-invariant effective gluon mass from the operator-product expansion' Physical Review D 44, (1) R26-R28 , DOI
Schaden M, Reinhardt H, Amundsen PA & Lavelle MJ 1990 'An effective action for Yang-Mills field strengths' Nuclear Physics B 339, (3) 595-622 , DOI
Lavelle M & Schaden M 1990 'The gluon condensate and the effective potential in QCD' Physics Letters B 246, (3-4) 487-492 , DOI
Lavelle M & Schaden M 1989 'Propagators and condensates for QCD in the axial gauge' Physics Letters B 217, (4) 551-559 , DOI
Lavelle MJ & Schaden M 1988 'Propagators and condensates in QCD' Physics Letters B 208, (2) 297-302 , DOI
Lavelle MJ, Schaden M & Vladikas A 1988 'Propagators and relaxation for stochastically quantised U(1) in the temporal gauge' Physics Letters B 203, (4) 441-448 , DOI
Tuite MP & Lavelle MJ 1987 'Stochastic quantisation and gauge fixing for non-abelian lattice gauge theories' Nuclear Physics B 290, 205-217 , DOI
Lautrup B, Lavelle MJ, Tuite MP & Vladikas A 1987 'Stochastic quantisation and gauge fixing in lattice gauge theories' Nuclear Physics B 290, 188-204 , DOI
Lavelle MJ 1985 'Sum rules for baryonic vertex functions and the proton wave function in QCD' Nuclear Physics B 260, (2) 323-332 , DOI
Lavelle MJ 1985 'QCD sum rules and pion wave functions' Zeitschrift f�r Physik C Particles and Fields 29, (2) 203-208 , DOI
Chapters
Bagan E, Horan R, Lavelle M & McMullan D 2002 'Charged particles: A builder's guide' in Fried HM; Gabellini Y; Muller B Proceedings of 6th Workshop on Nonperturbative Quantum Chromodynamics World Scientific 134-139
Bagan E, Lavelle M & McMullan D 2002 'Screening, anti-screening and confinement' in Fried HM; Gabellini Y; Muller B Proceedings of 6th Workshop on Nonperturbative Quantum Chromodynamics, World Scientific World Scientific 197-202
Conference Papers
Ilderton A, Heinzl T, Langfeld K, Lavelle M & McMullan D 2009 'Infra-red problems and a response'
Langfeld K, Heinzl T, Ilderton A, Lavelle M & McMullan D 2008 'Solution of the Gribov problem from gauge invariance'
Lavelle M 2007 'Charges in QED and QCD' 37-41
Horan R, Lavelle M, McMullan D & Khvedelidze A 2002 'Charges, monopoles and gauge invariance' Confinement, Topology and other Nonpreturbative Aspects of QCD, Kluwer Academic Publishers 205-212
Belt ST, Horan R & Lavelle M 2001 'LATEX/PDF support materials for learning mathematics' Variety in Chemistry Teaching, Lancaster University
Bagan E, Horan R, Lavelle M & McMullan D 1999 'The glue around quarks and the interquark potential' Elsevier BV 353-356 , DOI
Bagan E, Lavelle M & McMullan D 1998 'The glue around quarks and the infra-red' Elsevier BV 329-332 , DOI
Bagan E, Lavelle M, McMullan D, Fiol B & Roy N 1997 'How do constituent quarks arise in QCD? Perturbation theory and the infra-red' Elsevier BV 208-212 , DOI