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Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080957641
Category : Mathematics
Languages : en
Pages : 177
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Book Description
A Deductive Theory of Space and Time
Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080957641
Category : Mathematics
Languages : en
Pages : 177
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Book Description
A Deductive Theory of Space and Time
Author: J. Frölich
Publisher: Springer Science & Business Media
ISBN: 1461534720
Category : Science
Languages : en
Pages : 528
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Book Description
Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.
Author: Victoria Rimell
Publisher: Cambridge University Press
ISBN: 1316368602
Category : Literary Collections
Languages : en
Pages : 371
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Book Description
This ambitious book investigates a major yet underexplored nexus of themes in Roman cultural history: the evolving tropes of enclosure, retreat and compressed space within an expanding, potentially borderless empire. In Roman writers' exploration of real and symbolic enclosures - caves, corners, villas, bathhouses, the 'prison' of the human body itself - we see the aesthetic, philosophical and political intersecting in fascinating ways, as the machine of empire is recast in tighter and tighter shapes. Victoria Rimell brings ideas and methods from literary theory, cultural studies and philosophy to bear on an extraordinary range of ancient texts rarely studied in juxtaposition, from Horace's Odes, Virgil's Aeneid and Ovid's Ibis, to Seneca's Letters, Statius' Achilleid and Tacitus' Annals. A series of epilogues puts these texts in conceptual dialogue with our own contemporary art world, and emphasizes the role Rome's imagination has played in the history of Western thinking about space, security and dwelling.
Author: Nicola Arcozzi
Publisher: American Mathematical Soc.
ISBN: 1470450828
Category : Mathematics
Languages : en
Pages : 559
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Book Description
The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.
Author: Gian Luca Delzanno
Publisher: Frontiers Media SA
ISBN: 2889636593
Category :
Languages : en
Pages : 288
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Book Description
Author: Emmanuel Fricain
Publisher: Cambridge University Press
ISBN: 1107027772
Category : Mathematics
Languages : en
Pages : 703
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Book Description
This is volume 1 of a 2 volume set.
Author: Mou-Hsiung Chang
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110788195
Category : Computers
Languages : en
Pages : 426
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Book Description
This book provides an up-to-date account of current research in quantum information theory, at the intersection of theoretical computer science, quantum physics, and mathematics. The book confronts many unprecedented theoretical challenges generated by infi nite dimensionality and memory effects in quantum communication. The book will also equip readers with all the required mathematical tools to understand these essential questions.
Author:
Publisher:
ISBN:
Category : Large space structures (Astronautics)
Languages : en
Pages : 192
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Book Description
Author: Gerald Teschl
Publisher: American Mathematical Soc.
ISBN: 0821846604
Category : Mathematics
Languages : en
Pages : 322
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Book Description
Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).
Author: W. J. Padgett
Publisher: Springer
ISBN: 3540379045
Category : Mathematics
Languages : en
Pages : 116
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Book Description
