TY - JOUR
T1 - Quantum gauge symmetries in noncommutative geometry
Y1 - 2014
A1 - Jyotishman Bhowmick
A1 - Francesco D'Andrea
A1 - Biswarup Krishna Das
A1 - Ludwik Dabrowski
AB - We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite-dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms in the framework of compact quantum group theory and spectral triples. The quantum analogue of these groups are defined as universal (initial) objects in some natural categories. After proving the existence of the universal objects, we discuss several examples that are of interest to physics, as they appear in the noncommutative geometry approach to particle physics: in particular, the C*-algebras M n(R), Mn(C) and Mn(H), describing the finite noncommutative space of the Einstein-Yang-Mills systems, and the algebras A F = C H M3 (C) and Aev = H H M4(C), that appear in Chamseddine-Connes derivation of the Standard Model of particle physics coupled to gravity. As a byproduct, we identify a "free" version of the symplectic group Sp.n/ (quaternionic unitary group).
PB - European Mathematical Society Publishing House
UR - http://urania.sissa.it/xmlui/handle/1963/34897
U1 - 35182
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - Quantum Isometries of the finite noncommutative geometry of the Standard Model
JF - Commun. Math. Phys. 307:101-131, 2011
Y1 - 2011
A1 - Jyotishman Bhowmick
A1 - Francesco D'Andrea
A1 - Ludwik Dabrowski
AB - We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.
PB - Springer
UR - http://hdl.handle.net/1963/4906
U1 - 4688
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - JOUR
T1 - Quantum spin coverings and statistics
JF - J. Phys. A 36 (2003), no. 13, 3829-3840
Y1 - 2003
A1 - Ludwik Dabrowski
A1 - Cesare Reina
AB - SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail.
PB - IOP Publishing
UR - http://hdl.handle.net/1963/1667
U1 - 2451
U2 - Mathematics
U3 - Mathematical Physics
ER -