Covariant Quantum Fields on Noncommutative Spacetimes

Abstract

A spinless covariant field $\varphi$ on Minkowski spacetime $\M^{d+1}$ obeys the relation $U(a,\Lambda )\varphi (x)U(a,\Lambda {)}^{-1}=\varphi (\Lambda x+a)$ where $(a,\Lambda )$ is an element of the Poincaré group $\Pg$ and $U:(a,\Lambda )\to U(a,\Lambda )$ is its unitary representation on quantum vector states. It expresses the fact that Poincaré transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincaré 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 Moyal spacetimes are derived transparently. For the Voros algebra, covariance and the *-operation are in conflict so that there are no covariant Voros fields compatible with *, a result we found earlier. The notion of Drinfel'd twist underlying much of the preceding discussion is extended to discrete abelian and nonabelian groups such as the mapping class groups of topological geons. For twists involving nonabelian groups the emergent spacetimes are nonassociative.

20 pages

References in corpus (6)

• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Twisted Gauge Theories
• Non-Pauli Transitions From Spacetime Noncommutativity
• Non-Pauli Effects from Noncommutative Spacetimes
• Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent

Cited by in corpus (7)

• Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space
• Kinematic variables in noncommutative phase space and parameters of noncommutativity
• Noncommutative phase space with rotational symmetry and hydrogen atom
• Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane
• Features of free particles system motion in noncommutative phase space
• Quantum Geons and Noncommutative Spacetimes
• Features of description of composite system's motion in twist-deformed space-time