Lorentz symmetry breaking as a quantum field theory regulator

By Matt Visser. 2009

255 citations recorded by the source corpus.

Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ac1f487302d02df7c90b148c919abb48d69a5b77

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Citations in the corpus

Cosmology of the Lifshitz universe (2009, background): “Renormalizable theories with higher spatial derivatives were studied in [61, 62, 63] for scalars and fermions and in [64, 65] for gauge theories (see also [66] for a Lorentz-violating extension of the Standard Model).”
Quantum field theory, gravity and cosmology in a fractal universe (2010, background): “In the case of gravity also vertices contribute [3, 4], each with a factor of 2 (number of derivatives).”
Hořava–Lifshitz dark energy (2009, background): “Due to the these novel features, there has been a large amount of effort in examining and extending the properties of the theory itself [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31].”
Tests of Lorentz invariance: a 2013 update (2013, background): “It was shown that power-counting renormalizability requires the action to include terms with at least six spatial derivatives in four dimensions [76, 126].”
Relativistic Quantum Gravity at a Lifshitz Point (2009, unknown): “Contents”
Strong coupling in Horava gravity (2009, methodology): “J H E P 0 8 ( 2 0 0 9 ) 0 7 0 for L loops [18].”
Field theory at a Lifshitz point (2009, result): “1 A similar result was obtained in [13].”
Quantum gravity without Lorentz invariance (2009, background): “All of these theories should be well-behaved as quantum field theories [1, 4, 19].”
Spectral dimension of the universe in quantum gravity at a lifshitz point. (2009, background): “roduced in [12,13]. The case of Yang-Mills with z = 2 was discussed in [24]. – 3 – For power-counting renormalizability of gravity in 3 + 1 dimensions, we need z = 3 at short distances [13] (see also [25]). A theory of gravity in 3 + 1 dimensions with z = 3 was presented in [13]. The ﬁeld content co”