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In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics.
Lie algebras. --- Moduli theory. --- Fiber bundles (Mathematics) --- Functions, Theta. --- Conformal invariants. --- Affine algebraic groups.
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This Special Issue celebrates the opening of a new section of the journal Foundation: Physical Sciences. Theoretical and experimental studies related to various areas of fundamental physics are presented in this Special Issue. The published papers are related to the following topics: dark matter, electron impact excitation, second flavor of hydrogen atoms, quantum antenna, molecular hydrogen, molecular hydrogen ion, wave pulses, Brans-Dicke theory, hydrogen Rydberg atom, high-frequency laser field, relativistic mean field formalism, nonlocal continuum field theories, parallel universe, charge exchange, van der Waals broadening, greenhouse effect, strange and unipolar electromagnetic pulses, quasicrystals, Wilhelm-Weber’s electromagnetic force law, axions, photoluminescence, neutron stars, gravitational waves, diatomic molecular spectroscopy, information geometric measures of complexity. Among 21 papers published in this Special Issue, there are 5 reviews and 16 original research papers.
Research & information: general --- Physics --- information geometry --- complexity --- classical and quantum physics --- self-simulation hypothesis --- principle of efficient language --- quasicrystals --- empires --- game of life --- emergence --- state sum models --- space–time couplings --- spatiotemporal --- ultrafast optics --- unipolar pulses --- few cycle pulses --- line-by-line --- greenhouse effect --- radiative fluxes --- thermal emission --- spectroscopy --- stark broadening --- atomic physics --- foundations of quantum mechanics --- molecular spectroscopy --- diatomic molecules --- symmetry transformations --- optical emission spectroscopy --- astrophysics --- neutron stars --- nuclear equation of state --- gravitational waves --- speed of sound --- tidal polarizability --- charge exchange --- second flavor of hydrogen atoms --- dark matter --- stark effect --- parallel universes --- multiverse --- preferred direction in the universe --- bulk flow --- four spatial dimensions --- nonlocal metamaterials --- multiscale structures --- fiber bundles --- superspace --- mathematical methods --- mathematical physics --- nonlocal continuum field theory --- semiconductor materials --- preformed cluster decay --- relativistic mean-field --- alpha-particle clustering --- neck-length --- hydrogenic atoms --- high-frequency laser field --- relativistic precession --- laser-controlled precession --- cosmological constant --- generalised Brans-Dicke theory --- Big Rip --- photoluminescence --- dispersive media --- axion --- space-time couplings --- bipolar pulses --- few-cycle pulses --- free-space wave equation --- space-time wave packets --- nondiffracting localized waves --- molecular hydrogen ion --- proton collisions --- molecular spectral bands --- quantum antennas --- quantum field theory --- relativistic quantum mechanics --- quantum radiation --- propagator --- Green’s function --- quantum engineering --- quantum technologies --- radiation pattern --- electron impact excitation of hydrogen atoms --- discrepancy between theories and experiments --- electron impact excitation of hydrogen molecules --- quantum mechanics --- particle–wave duality --- quantum jump --- quantum entanglement --- Weber’s electrodynamics --- Weber force --- field theory --- electromagnetism --- electrodynamics --- physics of elementary particles and fields --- magnetic field --- electric field --- electrical engineering --- fundamental physics
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