Nonlinear Bogolyubov-Valatin transformations: two modes

DOI10.1016/j.aop.2011.05.001zbMath1252.81092arXiv1002.2737OpenAlexW3122143571MaRDI QIDQ649620

K. Scharnhorst, J. W. Van Holten

Publication date: 2 December 2011

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.2737

zbMATH Keywords

canonical transformationClifford algebrafermions\mathbb R\))group \(SO(6group \(SU(4)\)nonlinear Bogolyubov-Valatin transformationnonlinear spin transformation

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Axiomatic quantum field theory; operator algebras (81T05) Spinor and twistor methods applied to problems in quantum theory (81R25) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Clifford algebras, spinors (15A66) Operator algebra methods applied to problems in quantum theory (81R15)

Uses Software

• CLIFFORD

Cites Work

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• Normally related \(n\)-planes and isoclinic \(n\)-planes in \(R^{2n}\) and strongly linearly independent matrices of order \(n\)
• Multivectorial representation of Lie groups
• On the parametrization of the proper orthogonal group
• Clifford algebra to geometric calculus. A unified language for mathematics and physics
• Extended supersymmetric \(\sigma \)-model based on the \(SO(2N+1)\) Lie algebra of the fermion operators
• Twistors in geometric algebra
• On the exterior calculus of invariant theory
• An introduction to the spinorial chessboard
• Fixed bivectors at 4- dimensional rotations
• Generalised quaternion methods in conformal geometry
• Determinants and their applications in mathematical physics
• A nonlinear Bogolyubov transformation
• Multivector Dirac equation and \(\mathbb Z_2\)-gradings of Clifford algebras
• Isomorphism groups in Clifford algebras
• On parametrization of the linear \(\text{GL}(4,\mathbb{C})\) and unitary \(\text{SU}(4)\) groups in terms of Dirac matrices.
• Clifford algebras and representations of complex orthogonal groups
• On the SO(2N+1) Regular Representation of Operators and Wave Functions of Fermion Many-Body Systems
• The Group Theoretical Structure of Fermion Many-Body Systems Arising from the Canonical Anticommutation Relation. I: Lie Algebras of Fermion Operators and Exact Generator Coordinate Representations of State Vectors
• Note on the New Type of the SO(2N+1) Time-Dependent Hartree-Bogoliubov Equation
• An Equation for the Quasi-Particle RPA Based on the SO(2N + 1) Lie Algebra of the Fermion Operators
• Time Dependent SO(2N+1) Theory for Unified Description of Bose and Fermi Type Collective Excitations
• Lie groups as spin groups
• Properties of the Dirac Matrices
• Nonclassical Transformation in Special Relativity
• A representation theorem for real or complex bivectors
• Curvature operators which preserve normal spaces
• On Sets of Anticommuting Matrices
• Entanglement and tensor product decomposition for two fermions
• On Sets of Anticommuting Matrices. Part II: The Factorization of E -Numbers
• Note on the Anticommuting Matrices of Eddington
• Twistors and the conformal group
• The Dirac gamma matrices as ‘‘relics’’ of a hidden symmetry?: As fundamental representations of the algebra sp(4,R)
• A five-dimensional form of the Dirac equation
• A Remarkable Representation of the 3 + 2 de Sitter Group
• Dirac Algebra and the Six-Dimensional Lorentz Group
• Conformal Charge Conjugation
• Tensor Product Decomposition, Entanglement, and Bogoliubov Transformations for Two Fermion System
• On the Restricted Lorentz Group and Groups Homomorphically Related to It
• Quaternions in Relativity
• Isoclinic 𝑛-planes in Euclidean 2𝑛-space, Clifford parallels in elliptic (2𝑛-1)-space, and the Hurwitz matrix equations
• A Theorem Concerning Eddington's E -Numbers
• De Sitter quasigroups

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