Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products

Abstract

We present a comparison of the noncommutative field theories built using two different star products: Moyal and Wick-Voros (or normally ordered). For the latter we discuss both the classical and the quantum field theory in the quartic potential case, and calculate the Green's functions up to one loop, for the two and four points cases. We compare the two theories in the context of the noncommutative geometry determined by a Drinfeld twist, and the comparison is made at the level of Green's functions and S-matrix. We find that while the Green's functions are different for the two theories, the S-matrix is the same in both cases, and is different from the commutative case.

This is the merging of two previous postings: arXiv:0807.1492 and arXiv:0807.1498

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• On the $\star$-product quantization and the Duflo map in three dimensions
• Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent
• Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Translational-invariant noncommutative gauge theory
• Noncommutative deformations of quantum field theories, locality, and causality
• Translation-Invariant Noncommutative Renormalization
• Asymptotic commutativity of quantized spaces: the case of ${\mathbb{CP}}^{p,q}$
• Voros product and the Pauli principle at low energies
• Noncommutative Conformal Field Theory in the Twist-deformed context
• The Structure of Spacetime and Noncommutative Geometry
• Review of Twisted Poincare Symmetry