Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Picken, R. F."'
Autor:
Nelson, J. E., Picken, R. F.
Publikováno v:
Modern Physics Letters A, Vol 33, 1 (2019) 1950256 (8 pages), World Scientific
Quantum holonomies of closed paths on the torus $T^2$ are interpreted as elements of the Heisenberg group $H_1$. Group composition in $H_1$ corresponds to path concatenation and the group commutator is a deformation of the relator of the fundamental
Externí odkaz:
http://arxiv.org/abs/1808.08812
Autor:
Nelson, J. E., Picken, R. F.
We continue our investigation into intersections of closed paths on a torus, to further our understanding of the commutator algebra of Wilson loop observables in 2+1 quantum gravity, when the cosmological constant is negative. We give a concise revie
Externí odkaz:
http://arxiv.org/abs/1309.2187
Autor:
Nelson, J. E., Picken, R. F.
Publikováno v:
Gen.Rel.Grav.43:777-795,2011
Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their commutators describ
Externí odkaz:
http://arxiv.org/abs/1006.0921
Autor:
Nelson, J. E., Picken, R. F.
In the context of (2+1)--dimensional gravity, we use holonomies of constant connections which generate a $q$--deformed representation of the fundamental group to derive signed area phases which relate the quantum matrices assigned to homotopic loops.
Externí odkaz:
http://arxiv.org/abs/0903.4809
Autor:
Nelson, J. E., Picken, R. F.
Publikováno v:
J.Phys.A41:304011,2008
In the context of quantum gravity for spacetimes of dimension 2+1, we describe progress in the construction of a quantum Goldman bracket for intersecting loops on surfaces. Using piecewise linear paths in R^2 (representing loops on the spatial manifo
Externí odkaz:
http://arxiv.org/abs/0711.2271
Autor:
Nelson, J. E., Picken, R. F.
We describe some results concerning the phase space of 3-dimensional Einstein gravity when space is a torus and with negative cosmological constant. The approach uses the holonomy matrices of flat SL(2,R) connections on the torus to parametrise the g
Externí odkaz:
http://arxiv.org/abs/math-ph/0501051
Autor:
Nelson, J. E., Picken, R. F.
Publikováno v:
Adv.Theor.Math.Phys. 9 (2005) 407-433
In the context of (2+1)--dimensional quantum gravity with negative cosmological constant and topology R x T^2, constant matrix--valued connections generate a q--deformed representation of the fundamental group, and signed area phases relate the quant
Externí odkaz:
http://arxiv.org/abs/math-ph/0412007
Autor:
Nelson, J. E., Picken, R. F.
We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and upper--triang
Externí odkaz:
http://arxiv.org/abs/gr-qc/0408082
Autor:
Picken, R. F., Semiao, P. A.
We present a general framework for TQFT and related constructions using the language of monoidal categories. We construct a topological category C and an algebraic category D, both monoidal, and a TQFT functor is then defined as a certain type of mon
Externí odkaz:
http://arxiv.org/abs/math/0212310
Autor:
Nelson, J. E., Picken, R. F.
Publikováno v:
Lett.Math.Phys.59:215-226,2002
The moduli space of flat SL(2,R)-connections modulo gauge transformations on the torus may be described by ordered pairs of commuting SL(2,R) matrices modulo simultaneous conjugation by SL(2,R) matrices. Their spectral properties allow a classificati
Externí odkaz:
http://arxiv.org/abs/math-ph/0105015