2 edition of **Representations of quantum groups and q-deformed invariant wave equations** found in the catalog.

Representations of quantum groups and q-deformed invariant wave equations

V. K. Dobrev

- 199 Want to read
- 14 Currently reading

Published
**1995**
by Papierflieger in Clausthal-Zellerfeld
.

Written in English

- Quantum groups.,
- Wave equation.,
- Representations of groups.,
- Conformal invariants.

**Edition Notes**

Statement | V.K. Dobrev. |

Classifications | |
---|---|

LC Classifications | QC20.7.G76 D63 1995 |

The Physical Object | |

Pagination | 173 p. ; |

Number of Pages | 173 |

ID Numbers | |

Open Library | OL910851M |

ISBN 10 | 3930697599 |

LC Control Number | 95205986 |

The book discusses abstract group theory and invariant subgroups, including theorems of finite groups, factor group, and isomorphism and homomorphism. The text also reviews the algebra of representation theory, rotation groups, three-dimensional pure rotation group, and characteristics of . Topics Covered in this Video Segment. Quantum States, Kets and Eigenvalue Equations. Quantum Operators, Hermitian Operators, Basis States. Representations in Quantum Mechanics. Collapsing.

We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. Our methods are rooted in the bracket state sum model for the Jones polynomial. The Jordan–Schwinger realization of quantum algebra U ⌣ q (s u 2) is used to construct the irreducible submodule T l of the adjoint representation in two different bases. The two bases are known as types of irreducible tensor operators of rank l which are related to each other by the involution map. The bases of the submodules are equipped with q-analogues of the Hilbert–Schmidt inner.

The q-deformed boson realisation of the quantum group SU(n) q ((A n-1) q) is constructed and certain types of representations of SU(n) q are obtained in the q-deformed Fock space by this boson realisation. The Jimbo representations of the quantum group SU(2) q are given as an example in this letter. * Infinite Component Fields * Gravity: The Einstein, Einstein-Cartan and Metric-Affine Theories * The Double Covering of GL(4,R) * overline{SL}(4,{R}) and Its Representation * SL(2, ℂ)-Invariant Wave Equations * A Wave Equation Based on The Dirac Embedding * Appendix A: Limitations on X v AS overline{SL}(4, {R}) Fourvector * Appendix B: Dirac.

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Quantum Theory, Groups and Representations: An Introduction Peter Woit Department of Mathematics, Columbia University [email protected] Invariant Differential Operators, Volume 2: Quantum Groups Vladimir K. Dobrev With applications in quantum field theory, general relativity and elementary particle physics, this two-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras.

Quantum Groups and Deformed Quantum Systems. Quantum Groups as a Model of Quantized Space. Some Remarks on the q - Poincaré Algebra in R - Matrix Form. Symmetries of q - Deformed Heat Equations. q - Deformed Path Integral with Commuting and Non-Commuting Variables.

New q - Minkowski Space-Time and Generalized q - Maxwell Equations Hierarchies. In the last ten years there were many developments in the representation theory of those quantum groups q-Conformal Invariant Equations and q-Plane Wave Solutions q-deformed equations.

Author: Vladimir Dobrev. Books V.K. Dobrev, "Representations of Quantum Groups and q -Deformed Invariant Wave Equations", Dr. Habil. Thesis, Tech. Univ. Clausthal(Papierflieger Verlag, Clausthal-Zellerfeld, ) ISBN This chapter contains standard preparatory material.

We will present an overview of special relativity, relativistic Klein–Gordon and Dirac wave equations and the convention in this book for Dirac spinors, and a self-contained discussion of representation theory of the rotation and Lorentz groups.

In February at TU Clausthal I obtained the title Dr. Rer. Nat. Habil. with the thesis "Representations of Quantum Groups and q - Deformed Invariant Wave Equations". In January in Soﬂa I obtained the title Dr. Sci. (Doctor of Physical Sciences). From the beginning of I am Full Professor at the Institute in Soﬂa.

There are braided group analogs of all the classical simple Lie groups as well as braided matrix groups and braided matrices B(R) for every regular solution R of the quantum Yang–Baxter equations.

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For a first slogan (see here for slogan zero) I’ve chosen. Quantum theory is representation theory. One aspect of what I’m referring to is explained in detail in chapter 14 of these er you have a classical phase space (symplectic manifold to mathematicians), functions on the phase space give an infinite dimensional Lie algebra, with Poisson bracket the Lie bracket.

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the group of Lorentz transformations (). Quantum Knizhnik-Zamolodchikov equations and holomorphic vector bundles, Duke Math. J., v. 70(3),pp. Algebraic integrability of Macdonald operators and representations of quantum groups, q-algCompositio Math., v(), p Whittaker functions on quantum groups and q-deformed Toda operators, This is a book about representing symmetry in quantum mechanics.

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The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians.

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The irreps of D(K) and D(J), where J is the generator of rotations and K the generator of boosts, can be used to build to spin representations of the Lorentz group, because they are related to the spin matrices of quantum mechanics.

This allows them to derive relativistic wave equations. See also Associative algebras. Simple module. Topics covered include: unitary geometry, quantum theory (Schrödinger's wave equation, transition probabilities, directional quantization, collision phenomena, Zeeman and Stark effects); groups and their representations (sub-groups and conjugate classes, linear transformations, rotation and Lorentz groups, closed continuous groups, invariants.

This algebra is similar to the q-deformed SU(2) Lie algebra for the quantum S 2. Actually, our algebra is a q-analog of SU(2) (or SU(1, 1)) Lie algebra with ‘doubled' Cartan subalgebra (D, D ˜).

There may exist a quantum group symmetry associated with this new q-deformed Lie algebra. There is a similarlity to the case of quantum S 2.sentation theory, quantum groups, complete integrable systems and Nonlinear Conformally Invariant Wave Equations and Their Exact Solutions L.

BERKOVICH, Quantum Mechanics in Noninertial Reference Frames and Representations of the Euclidean Line Group G. SVETLICHNY, On Relativistic Non-linear Quantum.