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18
Oersted Medal Lecture 2002: Reforming the mathematical language of physics
 Am. J. Phys
, 2003
"... The connection between physics teaching and research at its deepest level can be illuminated by Physics Education Research (PER). For students and scientists alike, what they know and learn about physics is profoundly shaped by the conceptual tools at their command. Physicists employ a miscellaneous ..."
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Cited by 16 (4 self)
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The connection between physics teaching and research at its deepest level can be illuminated by Physics Education Research (PER). For students and scientists alike, what they know and learn about physics is profoundly shaped by the conceptual tools at their command. Physicists employ a miscellaneous assortment of mathematical tools in ways that contribute to a fragmentation of knowledge. We can do better! Research on the design and use of mathematical systems provides a guide for designing a unified mathematical language for the whole of physics that facilitates learning and enhances physical insight. This has produced a comprehensive language called Geometric Algebra, which I introduce with emphasis on how it simplifies and integrates classical and quantum physics. Introducing researchbased reform into a conservative physics curriculum is a challenge for the emerging PER community. Join the fun! I.
Set Theory and Physics
 FOUNDATIONS OF PHYSICS, VOL. 25, NO. 11
, 1995
"... Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of soli ..."
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Cited by 8 (7 self)
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Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (ChurchTurhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.
Paranjape, Recent mathematical developments in the Skyrme model, Phys. Reports 306
 15 J. Gladikowski and
, 1998
"... In this review we present a pedagogical introduction to recent, more mathematical developments in the Skyrme model. Our aim is to render these advances accessible to mainstream nuclear and particle physicists. We start with the static sector and elaborate on geometrical aspects of the definition of ..."
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Cited by 3 (0 self)
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In this review we present a pedagogical introduction to recent, more mathematical developments in the Skyrme model. Our aim is to render these advances accessible to mainstream nuclear and particle physicists. We start with the static sector and elaborate on geometrical aspects of the definition of the model. Then we review the instanton method which yields an analytical approximation to the minimum energy configuration in any sector of fixed baryon number, as well as an approximation to the surfaces which join together all the low energy critical points. We present some explicit results for B = 2. We then describe the work done on the multibaryon minima using rational maps, on the topology of the configuration space and the possible implications of Morse theory. Next we turn to recent work on the dynamics of Skyrmions. We focus exclusively on the low energy interaction, specifically the gradient flow method put forward by Manton. We illustrate the method with some expository toy models. We end this review with a presentation of our own work on the semiclassical quantization of nucleon states and low energy nucleonnucleon scattering. 1
The equation of a Light Leptonic Magnetic Monopole and its Experimental Aspects
"... The present theory is closely related to Dirac’s equation of the electron, but not to his magnetic monopole theory, except for his relation between electric and magnetic charge. The theory is based on the fact, that the massless Dirac equation admits a second electromagnetic coupling, deduced from a ..."
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Cited by 2 (0 self)
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The present theory is closely related to Dirac’s equation of the electron, but not to his magnetic monopole theory, except for his relation between electric and magnetic charge. The theory is based on the fact, that the massless Dirac equation admits a second electromagnetic coupling, deduced from a pseudoscalar gauge invariance. The equation thus obtained has the symmetry laws of a massless leptonic, magnetic monopole, able to interact weakly. We give a more precise form of the Dirac relation between electric and magnetic charges and a quantum form of the Poincaré first integral. In the Weyl representation our equation splits into Pconjugated monopole and antimonopole equations with the correct electromagnetic coupling and opposite chiralities, predicted by P. Curie. Charge conjugated monopoles are symmetric in space and not in time (contrary to the electric particles) : an important fact for the vacuum polarization. Our monopole is a magnetically excited neutrino, which leads to experimental consequences. These monopoles are assumed to be produced by electromagnetic pulses or arcs, leading to nuclear transmutations and, for beta radioactive elements, a shortening of the life time and the emission of monopoles instead of neutrinos in a magnetic field. A corresponding discussion is given in section 15. 1. Introduction.
On the electrodynamics of Minkowski at low velocities
, 2008
"... Abstract – The Galilean constitutive equations for the electrodynamics of moving media are derived for the first time. They explain all the historic and modern experiments which were interpreted so far in a relativistic framework assuming the constant light celerity principle. Here, we show the latt ..."
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Abstract – The Galilean constitutive equations for the electrodynamics of moving media are derived for the first time. They explain all the historic and modern experiments which were interpreted so far in a relativistic framework assuming the constant light celerity principle. Here, we show the latter to be sufficient but not necessary. Copyright c ○ EPLA, 2008 One century ago, Hermann Minkowski formulated, for the first time, a covariant theory of electrodynamics in moving media [1–4]. He generalized the studies of Henri Poincaré [5] and Albert Einstein [6] which were restricted to vacuum. The theory was not only a consequence of the relativity principle formulated by Poincaré but also of the constant light celerity principle formulated by Einstein. Hence, it should have been (and was) applied to the optics of moving media [7] and to fast particles in media [8]. Moreover, it was thought to be the only
Computer Physics Communications •• • (••••) •••–•••
"... JID:COMPHY AID:4018 /FLA [m5Gv1.5; v 1.35; Prn:12/02/2010; 8:53] P.1 (111) ..."
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JID:COMPHY AID:4018 /FLA [m5Gv1.5; v 1.35; Prn:12/02/2010; 8:53] P.1 (111)
Computer Physics Communications •• • (••••) •••–•••
"... JID:COMPHY AID:4068 /FLA [m5Gv1.5; v 1.38; Prn:3/05/2010; 12:51] P.1 (15) ..."
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JID:COMPHY AID:4068 /FLA [m5Gv1.5; v 1.38; Prn:3/05/2010; 12:51] P.1 (15)
EXCITATIONS OF GE ATOMS, MOLECULES AND NANOCLUSTERS USING COREPOLARIZATION POTENTIALS BY
"... In this thesis manybody Quantum Monte Carlo (QMC) calculations are presented for the ground state and excitation energies of Ge atoms, molecules, and clusters as large as Ge29H36 ( ≈ 1.2 nm diameter). The hydrogen terminated GenHm nanoclusters are of particular interest since they have optical prop ..."
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In this thesis manybody Quantum Monte Carlo (QMC) calculations are presented for the ground state and excitation energies of Ge atoms, molecules, and clusters as large as Ge29H36 ( ≈ 1.2 nm diameter). The hydrogen terminated GenHm nanoclusters are of particular interest since they have optical properties that are different from small molecules and bulk Ge, and are viewed as an ideal model for quantum confined semiconductor systems. The present QMC results are compared with previous QMC calculations for the corresponding Si molecules and clusters. In addition, the QMC gaps for GenHm are found to be higher than the gaps reported in recent timedependent density functional studies, by amounts similar to that previously found for Si systems. For materials containing Ge it is necessary to deal with the issue of correlation between the core and valence electrons. The accuracy of QMC for heavy atoms such as Ge (Z=32) is limited by the fact that the corevalence interactions cannot be treated at the same manybody level as the valencevalence interactions. Typically the corevalence interactions are treated at a singlebody level via a pseudopotential, but such methods are unsatisfactory for Ge which has a shallow, easily polarizable 3d core. Previous work has proposed using