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Books on the topic 'String: topological'

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Author: Grafiati

Published: 14 March 2023

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1

Hollands, Lotte. Topological strings and quantum curves. Amsterdam: Amsterdam University Press, 2009.

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2

W, Kolb Edward, Liddle Andrew R, United States. National Aeronautics and Space Administration., and Fermi National Accelerator Laboratory, eds. Topological defects in extended inflation. [Batavia, Ill.]: Fermi National Accelerator Laboratory, 1990.

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3

Chern-Simons theory, matrix models, and topological strings. Oxford: Clarendon Press, 2005.

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4

Block, Jonathan, 1960- editor of compilation, ed. String-Math 2011. Providence, Rhode Island: American Mathematical Society, 2012.

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5

Mathematical foundations of quantum field theory and perturbative string theory. Providence, R.I: American Mathematical Society, 2011.

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6

Vilenkin, A. Cosmic strings and other topological defects. Cambridge: Cambridge University Press, 1994.

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7

editor, Bouchard Vincent 1979, ed. String-Math 2014: June 9-13, 2014, University of Alberta, Alberta, Canada. Providence, Rhode Island: American Mathematical Society, 2016.

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8

editor, Donagi Ron, Douglas, Michael (Michael R.), editor, Kamenova Ljudmila 1978 editor, and Roček M. (Martin) editor, eds. String-Math 2013: Conference, June 17-21, 2013, Simons Center for Geometry and Physics, Stony Brook, NY. Providence, Rhode Island: American Mathematical Society, 2014.

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9

Berger, Ayelet. Temperature Driven Topological Switch in 1T’-MoTe2 and Strain Induced Nematicity in NaFeAs. [New York, N.Y.?]: [publisher not identified], 2018.

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10

Kaku, Michio. Strings, conformal fields, and topology: An introduction. New York: Springer-Verlag, 1991.

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11

1973-, Johnson Mark W., ed. A foundation for PROPs, algebras, and modules. Providence, Rhode Island: American Mathematical Society, 2015.

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12

1974-, Zomorodian Afra J., ed. Advances in applied and computational topology: American Mathematical Society Short Course on Computational Topology, January 4-5, 2011, New Orleans, Louisiana. Providence, R.I: American Mathematical Society, 2012.

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13

Hollands, Lotte. Topological Strings and Quantum Curves. Amsterdam University Press, 2010.

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14

Kostov, Ivan. String theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.31.

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This article discusses the link between matrix models and string theory, giving emphasis on topological string theory and the Dijkgraaf–Vafa correspondence, along with applications of this correspondence and its generalizations to supersymmetric gauge theory, enumerative geometry, and mirror symmetry. The article first provides an overview of strings and matrices, noting that the correspondence between matrix models and string theory makes it possible to solve both non-critical strings and topological strings. It then describes some basic aspects of topological strings on Calabi-Yau manifolds and states the Dijkgraaf–Vafa correspondence, focusing on how it is connected to string dualities and how it can be used to compute superpotentials in certain supersymmetric gauge theories. In addition, it shows how the correspondence extends to toric manifolds and leads to a matrix model approach to enumerative geometry. Finally, it reviews matrix quantum mechanics and its applications in superstring theory.

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15

Marino, Marcos. Chern-Simons Theory, Matrix Models, and Topological Strings. Oxford University Press, 2014.

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16

Marino, Marcos. Chern-Simons Theory, Matrix Models, and Topological Strings. Oxford University Press, 2005.

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17

Marino, Marcos. Chern-Simons Theory, Matrix Models, and Topological Strings. Oxford University Press, Incorporated, 2005.

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18

Shellard, E. P. S., Alexander Vilenkin, E. Paul S. Shellard, and A. Vilenkin. Cosmic Strings and Other Topological Defects. Cambridge University Press, 2000.

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19

Marino, Marcos. Chern-Simons Theory, Matrix Models, and Topological Strings. Oxford University Press, USA, 2005.

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20

Maeda, Yoshiaki, Motoko Kotani, and Hitoshi Moriyoshi. Noncommutative Geometry and Physics 4 - Workshop on Strings, Membranes and Topological Field Theory. World Scientific Publishing Co Pte Ltd, 2017.

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21

Pauly, Christian. Strong and Weak Topology Probed by Surface Science: Topological Insulator Properties of Phase Change Alloys and Heavy Metal Graphene. Springer London, Limited, 2016.

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22

Pauly, Christian. Strong and Weak Topology Probed by Surface Science: Topological Insulator Properties of Phase Change Alloys and Heavy Metal Graphene. Spektrum Akademischer Verlag GmbH, 2016.

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23

Hrushovski, Ehud, and François Loeser. An equivalence of categories. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0013.

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This chapter deduces from Theorem 11.1.1 an equivalence of categories between a certain homotopy category of definable subsets of quasi-projective varieties over a given valued field and a suitable homotopy category of definable spaces over the o-minimal Γ‎. The chapter introduces three categories that can be viewed as ind-pro definable and admit natural functors to the category TOP of topological spaces with continuous maps. The discussion is often limited to the subcategory consisting of A-definable objects and morphisms. The morphisms are factored out by (strong) homotopy equivalence. The chapter presents the proof of the equivalence of categories before concluding with remarks on homotopies over imaginary base sets.

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24

Davey, Kent. Magnetic field stimulation: the brain as a conductor. Edited by Charles M. Epstein, Eric M. Wassermann, and Ulf Ziemann. Oxford University Press, 2012. http://dx.doi.org/10.1093/oxfordhb/9780198568926.013.0005.

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For the purposes of magnetic stimulation, the brain can be treated as a homogeneous conductor. A properly designed brain stimulation system starts with the target stimulation depth, and it should incorporate the neural strength–duration response characteristics. Higher-frequency pulses require stronger electric fields. The background of this article is the theoretical base determining, where in the brain TMS induces electrical activity, and whether this shifts as a function of differences in the conductivity and organization of gray matter, white matter, and cerebrospinal fluid. The use of strong electric fields to treat many neurological disorders is well established. Both in the treatment of incontinence and clinical depression, the electric field should be sufficiently strong to initiate an action potential. The frequency, system voltage, capacitance, core stimulator size, and number of turns are treated as unknowns in a TMS stimulation design. This article presents the possible topological changes to be considered in the future.

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25

Hrushovski, Ehud, and François Loeser. The space of stably dominated types. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0003.

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This chapter introduces the space unit vector V of stably dominated types on a definable set V. It first endows unit vector V with a canonical structure of a (strict) pro-definable set before providing some examples of stably dominated types. It then endows unit vector V with the structure of a definable topological space, and the properties of this definable topology are discussed. It also examines the canonical embedding of V in unit vector V as the set of simple points. An essential feature in the approach used in this chapter is the existence of a canonical extension for a definable function on V to unit vector V. This is considered in the next section where continuity criteria are given. The chapter concludes by describing basic notions of (generalized) paths and homotopies, along with good metrics, Zariski topology, and schematic distance.

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26

Nelson, David R., and Ariel Amir. Defects on cylinders: superfluid helium films and bacterial cell walls. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198789352.003.0016.

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There is a deep analogy between the physics of crystalline solids and the behaviour of superfluids, dating back to the pioneering work of Phillip Anderson, Paul Martin, and others. The stiffness to shear deformations in a periodic crystal resembles the super-fluid density that controls the behaviour of supercurrents in neutral superfluids such as He4. Dislocations in solids have a close analogy with quantized vortices in superfluids. Remarkable recent experiments on the way rod-shaped bacteria elongate their cell walls have focused attention on the dynamics and interactions of point-like dislocation defects in partially-ordered cylindrical crystalline monolayers. In these lectures, we review the physics of superfluid helium films on cylinders and discuss how confinement in one direction affects vortex interactions with supercurrents. Although there are similarities with the way dislocations respond to strains on cylinders, important differences emerge due to the vector nature of the topological charges characterizing the dislocations.

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27

Butz, Martin V., and Esther F. Kutter. Multisensory Interactions. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780198739692.003.0010.

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This chapter shows that multiple sensory information sources can generally be integrated in a similar fashion. However, seeing that different modalities are grounded in different frames of reference, integrations will focus on space or on identities. Body-relative spaces integrate information about the body and the surrounding space in body-relative frames of reference, integrating the available information across modalities in an approximately optimal manner. Simple topological neural population encodings are well-suited to generate estimates about stimulus locations and to map several frames of reference onto each other. Self-organizing neural networks are introduced as the basic computation mechanism that enables the learning of such mappings. Multisensory object recognition, on the other hand, is realized most effectively in an object-specific frame of reference – essentially abstracting away from body-relative frames of reference. Cognitive maps, that is, maps of the environment are learned by connecting locations over space and time. The hippocampus strongly supports the learning of cognitive maps, as it supports the generation of new episodic memories, suggesting a strong relation between these two computational tasks. In conclusion, multisensory integration yields internal predictive structures about spaces and object identities, which are well-suited to plan, decide on, and control environmental interactions.

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28

Kenyon, Ian R. Quantum 20/20. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198808350.001.0001.

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This text reviews fundametals and incorporates key themes of quantum physics. One theme contrasts boson condensation and fermion exclusivity. Bose–Einstein condensation is basic to superconductivity, superfluidity and gaseous BEC. Fermion exclusivity leads to compact stars and to atomic structure, and thence to the band structure of metals and semiconductors with applications in material science, modern optics and electronics. A second theme is that a wavefunction at a point, and in particular its phase is unique (ignoring a global phase change). If there are symmetries, conservation laws follow and quantum states which are eigenfunctions of the conserved quantities. By contrast with no particular symmetry topological effects occur such as the Bohm–Aharonov effect: also stable vortex formation in superfluids, superconductors and BEC, all these having quantized circulation of some sort. The quantum Hall effect and quantum spin Hall effect are ab initio topological. A third theme is entanglement: a feature that distinguishes the quantum world from the classical world. This property led Einstein, Podolsky and Rosen to the view that quantum mechanics is an incomplete physical theory. Bell proposed the way that any underlying local hidden variable theory could be, and was experimentally rejected. Powerful tools in quantum optics, including near-term secure communications, rely on entanglement. It was exploited in the the measurement of CP violation in the decay of beauty mesons. A fourth theme is the limitations on measurement precision set by quantum mechanics. These can be circumvented by quantum non-demolition techniques and by squeezing phase space so that the uncertainty is moved to a variable conjugate to that being measured. The boundaries of precision are explored in the measurement of g-2 for the electron, and in the detection of gravitational waves by LIGO; the latter achievement has opened a new window on the Universe. The fifth and last theme is quantum field theory. This is based on local conservation of charges. It reaches its most impressive form in the quantum gauge theories of the strong, electromagnetic and weak interactions, culminating in the discovery of the Higgs. Where particle physics has particles condensed matter has a galaxy of pseudoparticles that exist only in matter and are always in some sense special to particular states of matter. Emergent phenomena in matter are successfully modelled and analysed using quasiparticles and quantum theory. Lessons learned in that way on spontaneous symmetry breaking in superconductivity were the key to constructing a consistent quantum gauge theory of electroweak processes in particle physics.

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