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Covariant Quantum Fields On Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Covariant Quantum Fields On Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Physics - All Scholarship
A spinless covariant field $\phi$ on Minkowski spacetime $\M^{d+1}$ obeys the relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where $(a,\Lambda)$ is an element of the Poincar\'e group $\Pg$ and $U:(a,\Lambda)\to U(a,\Lambda)$ is its unitary representation on quantum vector states. It expresses the fact that Poincar\'e transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincar\'e transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes. In this way all our earlier results on dressing, statistics, etc. for …
Quantum Geons And Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Quantum Geons And Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Physics - All Scholarship
Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincare group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter is not appropriate for more complicated spacetimes such as those containing the Friedman-Sorkin (topological) geons. They have rich diffeomorphism groups and in particular mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group SN. We generalise the Drinfel'd twist to (essentially) generic groups including to finite and discrete ones and use it to modify the …
Regge Calculus As A Fourth Order Method In Numerical Relativity, Mark A. Miller
Regge Calculus As A Fourth Order Method In Numerical Relativity, Mark A. Miller
Physics - All Scholarship
The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge equations converge to zero as the second power of the lattice spacing, but that an average over local Regge equations converges to zero as (at the very least) the third power of the lattice spacing. Numerical studies using analytic solutions to the Einstein equations show …
Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali
Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali
Physics - All Scholarship
We present a unified description of gravity and electromagnetism in the framework of a Z 2 non-commutative differential calculus. It can be considered as a “discrete version” of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory.
The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz
The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz
Physics - All Scholarship
The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P; Q \Gamma ] = 1, with P and Q \Gamma 2 \Theta 2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations …