Identical Particles and Quantum Symmetries

Abstract

We propose a solution to the problem of compatibility of Bose-Fermi statistics with symmetry transformations implemented by compact quantum groups of Drinfel'd type. We use unitary transformations to conjugate multi-particle symmetry postulates, so as to obtain a twisted realization of the symmetric groups S_n.

latex, 30 pages; final version (Nucl. Phys. B, in print)

References in corpus (11)

• Braided Momentum Structure of the q-Poincare Group
• Bicovariant Quantum Algebras and Quantum Lie Algebras
• Twisted Classical Poincaré Algebras
• Thermodynamic q-Distributions That Aren't
• The $S{O}_q(N,\mathbf{R})$-Symmetric Harmonic Oscillator on the Quantum Euclidean Space ${\mathbf{R}}_q^N$ and its Hilbert Space Structure
• The Euclidean Hopf algebra $U_q(e^N)$ and its fundamental Hilbert space representations
• Altering the Symmetry of Wavefunctions in Quantum Algebras and Supersymmetry
• More on quantum groups from the the quantization point of view
• The Hilbert Space Representations for SO_q(3)-symmetric quantum mechanics
• On the Drinfel'd-Kohno Equivalence of Groups and Quantum Groups
• Deformation Quantization of the Heisenberg Group

Cited by in corpus (29)

• Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Field Theory on the q-deformed Fuzzy Sphere I
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Noncommutative field theory with the Wick-Voros product
• Remarks on twisted noncommutative quantum field theory
• Field Theory on the q-deformed Fuzzy Sphere II: Quantization
• Quantum Fields on the Groenewold-Moyal Plane
• On second quantization on noncommutative spaces with twisted symmetries
• Deforming Maps for Lie Group Covariant Creation and Annihilation Operators
• Effects of Twisted Noncommutativity in Multi-particle Hamiltonians
• Deformed Kac-Moody and Virasoro Algebras
• Z^0 \to 2γand the Twisted Coproduct of the Poincaré Group
• Star Product Geometries
• On the Drinfel'd-Kohno Equivalence of Groups and Quantum Groups
• Quantum Theory, Noncommutativity and Heuristics
• Noncommutative Conformal Field Theory in the Twist-deformed context
• Separation of noncommutative differential calculus on quantum Minkowski space
• Reconstruction of universal Drinfeld twists from representations
• Noncommutative Geometry: Fuzzy Spaces, the Groenewold-Moyal Plane
• Learning from Julius' star, *, $\star$
• Field theoretic models on covariant quantum spaces
• Drinfeld twist for quantum $su(2)$ in the adjoint representation
• Thermal effective potential in two- and three- dimensional non-commutative spaces
• Remarks on SU_q(2) fermions
• On the braided Fock spaces
• Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space
• Noncommutative spaces with twisted symmetries and second quantization