Perturbative self-interacting scalar field theory: a differential equation approach
ABSTRACT We revisit the investigation about the partition function related to a \phi^4-scalar field theory on a n-dimensional Minkowski spacetime, which is shown to be a self-interacting scalar field theory at least in 4-dimensional Minkowski spacetime. After rederiving the analytical calculation of the perturbative expansion coefficients and also the approximate values for suitable limits using Stirling's formulae, which consists of Witten's proposed questions, solved by P. Deligne, D. Freed, L. Jeffrey, and S. Wu, we investigate a spherically symmetric scalar field in a n-dimensional Minkowski spacetime. For the first perturbative expansion coefficient it is shown how it can be derived a modified Bessel equation (MBE), which solutions are investigated in one, four, and eleven-dimensional Minkowski spacetime. The solutions of MBE are the first expansion coefficient of the series associated with the partition function of \phi^4-scalar field theory. All results are depicted.
Full-textDOI: · Available from: Edmundo Capelas de Oliveira, Feb 17, 2014
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ABSTRACT: In the framework of a five-dimensional model with one 3-brane and an infinite extra dimension, we discuss a process in which matter escapes from the brane and propagates into the bulk to arbitrarily large distances. An example is a decay of a particle of mass $2m$ residing on the brane into two particles of mass $m$ that leave the brane and accelerate away. We calculate, in the linearized theory, the metric induced by these particles on the brane. This metric does not obey the four-dimensional Einstein equations and corresponds to a spherical gravity wave propagating along the four-dimensional future light cone. The four-dimensional space-time left behind the spherical wave is flat, so the gravitational field induced in the brane world by matter escaping from the brane disappears in a causal way. Comment: 14 pages of LaTeX, no figuresClassical and Quantum Gravity 03/2000; 17(21). DOI:10.1088/0264-9381/17/21/306 · 3.10 Impact Factor
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ABSTRACT: We propose an alternative theoretical approach showing how the existence of an extra dimension in Randall-Sundrum model can estimate the correction in the horizon of Schwarzschild and Kerr black holes, and consequently its measurability in terms of the variation of quasar luminosity, which can be caused by a imprint of an extra dimension endowing the geometry of a brane-world scenario in an AdS5 bulk. The rotation effects cause a more prominent correction in Kerr horizon radius than in Schwarzschild (static black hole) radius, via brane-world effects, and the consequent bigger variation in the luminosity in Kerr black holes quasars. This paper is intended to investigate the variation of luminosity due to accretion of gas in Schwarzschild and Kerr black holes (BHs) in the center of quasars, besides also investigating the variation of luminosity in supermassive BHs by brane-world effects, using Randall-Sundrum model.Journal of Cosmology and Astroparticle Physics 10/2005; 2005(12). DOI:10.1088/1475-7516/2005/12/009 · 5.88 Impact Factor
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