Nonlocal regularisation of noncommutative field theories

Govindarajan, T. R.
Kürkcüoğlu, Seçkin
We study noncommutative field theories, which are inherently nonlocal, using a Poincare-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cutoff scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention on the particular case when the noncommutativity parameter is inversely proportional to the square of the cutoff, via a dimensionless parameter eta. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in eta-dependent terms. The implications of this approach, which avoids the problems related to uv-ir mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories.


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Using the Nikiforov-Uvarov method which is based on solving the second-order differential equations, we firstly analyzed the energy spectra and eigenfunctions of the Woods-Saxon potential. In the framework of the PT-symmetric quantum mechanics, we secondly solved the time-independent Schrodinger equation for the PT and non-PT-symmetric version of the potential. It is shown that the discrete energy eigenvalues of the non-PT-symmetric potential consist of the real and imaginary parts, but the PT-symmetric one...
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We give an explicitly gauge-invariant canonical analysis of linearized quadratic gravity theories in three dimensions for both flat and de Sitter backgrounds. In flat backgrounds, we also study the effects of the gravitational Chern-Simons term, include the sources, and compute the weak field limit as well as scattering between spinning massive particles.
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We first review the spontaneous Lorentz symmetry breaking in the presence of mass-less gauge fields and infraparticles. This result was obtained long time ago in the context of rigorous quantum field theory (QFT) by Frohlich, Morchio and Strocchi [Ann. Phys. 119, 241 (1979); Phys. Lett. B 89, 61 (1979)] and reformulated by Balachandran and Vaidya (arXiv:1302.3406) using the notion of superselection sectors and directiondependent test functions at spatial infinity for gauge transformations. Inspired by these...
Citation Formats
T. R. Govindarajan, S. Kürkcüoğlu, and M. PANERO, “Nonlocal regularisation of noncommutative field theories,” MODERN PHYSICS LETTERS A, pp. 1851–1863, 2006, Accessed: 00, 2020. [Online]. Available: