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Seen by:Arithmetic of Potts Model Hypersurfaces
by Jessica Su
We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition... more We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with the graph hypersurfaces of perturbative quantum field theory defined by the Kirchhoff graph polynomial. We give a very simple example of the failure of the "fibration condition" in the dependence of the Grothendieck class on the number of spin states and of the polynomial countability condition for these Potts model hypersurfaces. We then show that a period computation, formally similar to the parametric Feynman integrals of quantum field theory, arises by considering certain thermodynamic averages. One can show that these evaluate to combinations of multiple zeta values for Potts models on polygon polymer chains, while silicate tetrahedral chains provide a candidate for a possible occurrence of non-mixed Tate periods.
Inroduction to Cobordism Categories and TQFTs
by Shay Logan
This paper is a hand-wavy and overly general introduction to cobordism theory and TQFTs
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Seen by:Truth and Physics Education.
by Robert Shaw
Robert Keith Shaw (2010). Truth and Physics Education. Doctoral dissertation, University of Auckland
This thesis develops a hermeneutic philosophy of science to provide insights into physics education. -/- Modernity... more This thesis develops a hermeneutic philosophy of science to provide insights into physics education. -/- Modernity cloaks the authentic character of modern physics whenever discoveries entertain us or we judge theory by its use. Those who justify physics education through an appeal to its utility, or who reject truth as an aspect of physics, relativists and constructivists, misunderstand the nature of physics. Demonstrations, not experiments, reveal the essence of physics as two characteristic engagements with truth. First, truth in its guise as correspondence enables a human being to prepare for the distinctive event of physics. Second, the event of physics occurs in human perception when someone forces a hidden reality to disclose an aspect of itself. Thus, the ground of physics is our human involvement with reality achieved by way of truth. To support this account of physics, the thesis reports phenomenological investigations into Isaac Newton’s involvement with optics and a secondary school physics laboratory. These involve interpretations of Heidegger’s theory of beings, schema and signification. The project draws upon, and contributes to, the hermeneutic phenomenology of modern physics, a tradition in continental philosophy that begins with Immanuel Kant, and advances particularly from Martin Heidegger to Patrick Heelan. The thesis advocates an ontological pedagogy for modern physics which has as its purpose each individual student’s engagement with reality and truth. Students may achieve this through demonstrations of phenomena that will enable them to dwell with physics, an experience that contrasts with their embroilment in modernity, and which perpetuates nature’s own science.
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Seen by: and 3 more13 views
Seen by:Hopf maps and Wigner's little groups
Co-authored with Ruben Mkrtchyan and Armen Nersessian
We present the explicit formulae relating Hopf maps with Wigner’s little groups. They, particularly, explain simple... more We present the explicit formulae relating Hopf maps with Wigner’s little groups. They, particularly, explain simple action of group on a fiber for the first and second Hopf fibrations, and present most simplified form for the third one. Corresponding invariant Lagrangians are presented, and their possible reductions are discussed.
Action-angle variables for dihedral systems on the circle
Co-authored with Olaf Lechtenfeld, Armen Nersessian, published in Physics Letters A 374 (2010) 4647–4652
A nonrelativistic particle on a circle and subject to a cos^{-2}(k phi) potential is related to the two-dimensional... more A nonrelativistic particle on a circle and subject to a cos^{-2}(k phi) potential is related to the two-dimensional (dihedral) Coxeter system I_2(k), for k in N. For such `dihedral systems' we construct the action-angle variables and establish a local equivalence with a free particle on the circle. We perform the quantization of these systems in the action-angle variables and discuss the supersymmetric extension of this procedure. By allowing radial motion one obtains related two-dimensional systems, including A_2, BC_2 and G_2 three-particle rational Calogero models on R, which we also analyze.
Quantum ring models and action-angle variables
Co-authored with Stefano Bellucci, Armen Nersessian and Armen Saghatelian
We suggest to use the action-angle variables for the study of properties of (quasi)particles in quantum
rings.... more
We suggest to use the action-angle variables for the study of properties of (quasi)particles in quantum
rings. For this purpose we present the action-angle variables for three two-dimensional singular oscillator
systems. The first one is the usual (Euclidean) singular oscillator, which plays the role of the confinement
potential for the quantum ring. We also propose two singular spherical oscillator models for the role of
the confinement system for the spherical ring. The first one is based on the standard Higgs oscillator
potential. We show that, in spite of the presence of a hidden symmetry, it is not convenient for the study
of the system’s behaviour in a magnetic field. The second model is based on the so-called CP1 oscillator
potential and respects the inclusion of a constant magnetic field.
Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere
Co-authored with Stefano Bellucci, Francesco Toppan, published in J.Phys.A43:045205,2010
Using the second Hopf map, we perform the reduction of the eight-dimensional (pseudo)spherical (Higgs)oscillator to a... more Using the second Hopf map, we perform the reduction of the eight-dimensional (pseudo)spherical (Higgs)oscillator to a five-dimensional system interacting with a Yang monopole. Then, using a standard trick, we obtain, from the latter system, the pseudospherical and spherical generalizations of the Yang-Coulomb system (the five dimensional analog of MICZ-Kepler system). We present the whole set of its constants of motions, including the hidden symmetry generators given by the analog of Runge-Lenz vector. In the same way, starting from the eight-dimensional anisotropic inharmonic Higgs oscillator, we construct the integrable (pseudo)spherical generalization of the Yang-Coulomb system with the Stark term.

