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890
Quantum chromodynamics and other field theories on the light cone, Phys. Rept. 301
, 1998
"... In recent years lightcone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground s ..."
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Cited by 34 (9 self)
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In recent years lightcone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground state of the full theory. We discuss the lightcone quantization of gauge theories from two perspectives: as a calculational tool for representing hadrons as QCD boundstates of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The lightcone Fock state expansion of wavefunctions provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of lightcone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavyquark contributions to structure functions. A general nonperturbative method for numerically solving quantum field theories, “discretized lightcone quantization”, is outlined and applied to several gauge theories. This method is invariant under the
Field Theory on a Supersymmetric Lattice
, 1995
"... A latticetype regularization of the supersymmetric field theories on a supersphere is constructed by approximating the ring of scalar superfields by an integervalued sequence of finite dimensional rings of supermatrices and by using the differencial calculus of noncommutative geometry. The regula ..."
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Cited by 28 (3 self)
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A latticetype regularization of the supersymmetric field theories on a supersphere is constructed by approximating the ring of scalar superfields by an integervalued sequence of finite dimensional rings of supermatrices and by using the differencial calculus of noncommutative geometry. The regulated theory involves only finite number of degrees of freedom and is manifestly supersymmetric. CERNTH/95195 July 1995 1 Part of Project No. P8916PHY of the `Fonds zur Forderung der wissenschaftlichen Forschung in Ostereich'. 1 Introduction The idea that a fine structure of spacetime should be influenced by quantum gravity phenomena is certainly not original but so far there was a little success in giving it more quantitative expression. String theory constitutes itself probably the most promising avenue to a consistent theory of quantum gravity it is therefore of obvious interest to study the structure of spacetime from the point of view. Though string theory incorporates a minimal ...
Spatiotemporal chaos and vacuum fluctuations of quantized fields, World Scientific
, 2002
"... We consider deterministic chaotic models of vacuum fluctuations on a small (quantum gravity) scale. As a suitable smallscale dynamics, nonlinear versions of strings, socalled ‘chaotic strings ’ are introduced. These can be used to provide the ‘noise ’ for second quantization of ordinary strings vi ..."
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Cited by 25 (14 self)
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We consider deterministic chaotic models of vacuum fluctuations on a small (quantum gravity) scale. As a suitable smallscale dynamics, nonlinear versions of strings, socalled ‘chaotic strings ’ are introduced. These can be used to provide the ‘noise ’ for second quantization of ordinary strings via the ParisiWu approach of stochastic quantization. Extensive numerical evidence is presented that the vacuum energy of chaotic strings is minimized for the numerical values of the observed standard model parameters, i.e. in this extended approach to second quantization concrete predictions for vacuum expectations of dilatonlike fields and hence on masses and coupling constants can be given. Lowenergy fermion and boson masses are correctly obtained with a precison of 34 digits, the electroweak and strong coupling strengths with a precison of 45 digits. In particular, the minima of the vacuum energy yield highprecision predictions of the Higgs mass (154 GeV), of the neutrino masses (1.45 · 10 −5 eV, 2.57 ·10 −3 eV, 4.92 ·10 −2 eV) and of the GUT scale (1.73 ·10 16 GeV).The following text is preface, introduction, (detailed) summary, and bibliography
The meanfield approximation in quantum electrodynamics. The nophoton case
 Comm. Pure Applied Math
"... We study the meanfield approximation of Quantum Electrodynamics, by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normalordering or choice of bare electron/positron subspaces. Neglecting photons, we define properly this Hamiltonian in a fi ..."
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Cited by 24 (11 self)
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We study the meanfield approximation of Quantum Electrodynamics, by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normalordering or choice of bare electron/positron subspaces. Neglecting photons, we define properly this Hamiltonian in a finite box [−L/2; L/2) 3, with periodic boundary conditions and an ultraviolet cutoff Λ. We then study the limit of the ground state (i.e. the vacuum) energy and of the minimizers as L goes to infinity, in the HartreeFock approximation. In case with no external field, we prove that the energy per volume converges and obtain in the limit a translationinvariant projector describing the free HartreeFock vacuum. We also define the energy per unit volume of translationinvariant states and prove that the free vacuum is the unique minimizer of this energy. In the presence of an external field, we prove that the difference between the minimum energy and the energy of the free vacuum converges as L goes to infinity. We obtain in the limit the socalled BogoliubovDiracFock functional. The HartreeFock (polarized) vacuum is a HilbertSchmidt perturbation of the free vacuum and it minimizes the BogoliubovDiracFock energy. 1
The electronic properties of graphene
 Rev. Mod. Phys. 2009
"... This article reviews the basic theoretical aspects of graphene, a oneatomthick allotrope of carbon, with unusual twodimensional Diraclike electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or t ..."
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Cited by 24 (0 self)
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This article reviews the basic theoretical aspects of graphene, a oneatomthick allotrope of carbon, with unusual twodimensional Diraclike electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge �surface � states in graphene depend on the edge termination �zigzag or armchair � and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electronelectron and electronphonon interactions in single layer and multilayer graphene are also
Learning in Boltzmann Trees
 Neural Computation
, 1995
"... We introduce a large family of Boltzmann machines that can be trained using standard gradient descent. The networks can have one or more layers of hidden units, with treelike connectivity. We show how to implement the supervised learning algorithm for these Boltzmann machines exactly, without resor ..."
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Cited by 24 (3 self)
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We introduce a large family of Boltzmann machines that can be trained using standard gradient descent. The networks can have one or more layers of hidden units, with treelike connectivity. We show how to implement the supervised learning algorithm for these Boltzmann machines exactly, without resort to simulated or meanfield annealing. The stochastic averages that yield the gradients in weight space are computed by the technique of decimation. We present results on the problems of Nbit parity and the detection of hidden symmetries. 1 Introduction Boltzmann machines (Ackley, Hinton, & Sejnowski, 1985) have several compelling virtues. Unlike simple perceptrons, they can solve problems that are not linearly separable. The learning rule, simple and locally based, lends itself to massive parallelism. The theory of Boltzmann learning, moreover, has a solid foundation in statistical mechanics. Unfortunately, Boltzmann machines as originally conceivedalso have some serious drawbacks...
QED Hopf algebras on planar binary trees
 Preprint 2001/15 of Institut Girard Desargues, arXiv:math.QA/0112043
"... In this paper we describe the Hopf algebras on planar binary trees used to renormalize the Feynman propagators of quantum electrodynamics, and the coaction which describes the renormalization procedure. Both structures are related to some semidirect coproduct of Hopf algebras. 1 ..."
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Cited by 22 (4 self)
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In this paper we describe the Hopf algebras on planar binary trees used to renormalize the Feynman propagators of quantum electrodynamics, and the coaction which describes the renormalization procedure. Both structures are related to some semidirect coproduct of Hopf algebras. 1
HEISENBERG–EULER EFFECTIVE LAGRANGIANS: BASICS AND EXTENSIONS
"... I present a pedagogical review of Heisenberg–Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum electrodynamics in a constant electromagnetic background field, and then summarizing some of the important a ..."
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Cited by 21 (2 self)
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I present a pedagogical review of Heisenberg–Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum electrodynamics in a constant electromagnetic background field, and then summarizing some of the important applications and generalizations to inhomogeneous background fields, nonabelian backgrounds, and higher loop effective Lagrangians.