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Tuesday, August 4, 2020 | History

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

Representations of quantum groups and q-deformed invariant wave equations

by V. K. Dobrev

  • 199 Want to read
  • 14 Currently reading

Published by Papierflieger in Clausthal-Zellerfeld .
Written in English

    Subjects:
  • Quantum groups.,
  • Wave equation.,
  • Representations of groups.,
  • Conformal invariants.

  • Edition Notes

    StatementV.K. Dobrev.
    Classifications
    LC ClassificationsQC20.7.G76 D63 1995
    The Physical Object
    Pagination173 p. ;
    Number of Pages173
    ID Numbers
    Open LibraryOL910851M
    ISBN 103930697599
    LC Control Number95205986

    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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Representations of quantum groups and q-deformed invariant wave equations by V. K. Dobrev Download PDF EPUB FB2

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.

Invariant Metrie and Invariant Measure on Lie Groups § Comments and Supplements § Exercises GROUP THEORY AND GROUP REPRESENTATIONS IN QUANTUM THEORY § 1.

Group Representations in Physics Relativistic Wave Equations and Induced Representations. Finite Component Relativistic Wave Equations Majorana was an expert in group theory. He had in his bookshelf the Weyl’s book on Quantum Mechanics and group theory [6], as well as other books more mathematically oriented in the sub-ject.

In particular in Weyl’s book one can find the calculatio n of the matrix elements in the angular momentum basis of the electric dipole operator.

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.

Highest weight representations of semisimple Lie algebras 4 Induced representations 4 Unitary Representations of the Lorentz and Poincar e groups 4 Representations of supersymmetry algebras 4 Nonlinear sigma models: Quantum eld theories de ned by group manifolds and homogeneous spaces.

Eugene Wigner won the Nobel Prize in Physics, in part due to his contributions to symmetry principles in physics.

In reading other books on group theory and quantum physics, you usually find a large number of references to Wigner's book. In fact, other books often state a theorem and then refer to Wigner's book for the s: 7.

Intuitive meaning. The discovery of quantum groups was quite unexpected since it was known for a long time that compact groups and semisimple Lie algebras are "rigid" objects, in other words, they cannot be "deformed". One of the ideas behind quantum groups is that if we consider a structure that is in a sense equivalent but larger, namely a group algebra or a universal enveloping algebra.

The Three Pictures of Quantum Mechanics Schrödinger • Quantum systems are regarded as wave functions which solve the Schrödinger equation. • Observables are represented by Hermitian operators which act on the wave function.

• In the Schrödinger picture, the operators stay fixed while the Schrödinger equation changes the basis with time. derivation of the two most widely used and best known Lorentz{invariant eld equations, namely the Klein{Gordon (Sect. ) and the Dirac (Sect.

) equation. Natural Representation of the Lorentz Group In this Section we consider the natural representation of the Lorentz group L, i.e.

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.

The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor.

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.

This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics.

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.