Aiyalam P. Balachandran et al JHEP11(2004)068 doi:10.1088/1126-6708/2004/11/068
Time-space noncommutativity: quantised evolutions
Aiyalam P. Balachandran1, Thupil R. Govindarajan2, Andrey Gomes Martins3 and Paulo Teotonio-Sobrinho3
Show affiliationsIn previous work [7], we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al. [1]. Here we extend it to certain noncommutative versions of the cylinder, 
3 and × S3. In all these models, only discrete time translations are possible, a result known before in the first two cases [2]–[6]. One striking consequence of quantised time translations is that even though a time independent hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing a and length L = Na, only momentum mod 2π/L is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined.
- Keywords
-
E-print Number: hep-th/0410067
Cited: by |
Refers: to
- PACS
- Subjects
- Dates
-
Issue 11 (November 2004)
Received 18 October 2004, accepted for publication 24 November 2004
Published 4 January 2005
-
Time-space noncommutativity: quantised evolutions
Aiyalam P. Balachandran et al JHEP11(2004)068
-
Activity measurements of the radionuclide 99Tcm for the PTB, Germany in the ongoing comparison BIPM.RI(II)-K1.Tc-99m
G Ratel et al 2006 Metrologia 43 06004
-
New constraints on Planck-scale Lorentz violation in QED from the Crab Nebula
Luca Maccione et al JCAP10(2007)013
-
Dissipation in circuit quantum electrodynamics: lasing and cooling of a low-frequency oscillator
Julian Hauss et al 2008 New J. Phys. 10 095018
-
Final report on subsequent key comparison CCQM-K18.1: pH of carbonate buffer
L Vyskocil et al 2008 Metrologia 45 08014
-
CCQM-P29 pilot study. Cadmium and zinc amount content in rice
Y Aregbe and P Taylor 2003 Metrologia 40 08002
-
CCQM-K32 key comparison and P84 pilot study: Amount of silicon oxide as a thickness of SiO2 on Si
M P Seah 2008 Metrologia 45 08013
-
Constraints on supersymmetric grand unified theories from cosmology
Jonathan Rocher and Mairi Sakellariadou JCAP03(2005)004
-
Inhomogeneous coupling in two-channel asymmetric simple exclusion processes
K Tsekouras and A B Kolomeisky 2008 J. Phys. A: Math. Theor. 41 095002
-
Final Report on CCT-K7: Key comparison of water triple point cells
M Stock et al 2006 Metrologia 43 03001
, and Chern–Simons–Higgs solitons on 
: dimensional reduction of Chern–Pontryagin densities