Related papers: One-loop corrections to the spectral action
We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of…
We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the…
One-loop effective action of noncommutative scalar field theory with cubic self-interaction is studied. Utilizing worldline formulation, both planar and nonplanar part of the effective action are computed explicitly. We find complete…
The massless QCD Lagrangian is conformally invariant and, as a consequence, so are the tree-level scattering amplitudes. However, the implications of this powerful symmetry at loop level are only beginning to be explored systematically.…
Using the formalism of superconnections, we show the existence of a bosonic action functional for the standard K-cycle in noncommutative geometry, giving rise, through the spectral action principle, only to the Einstein gravity and Standard…
In this paper I discuss connections between the noncommutative geometry approach to the standard model on one side, and the internal space coming from strings on the other. The standard model in noncommutative geometry is described via the…
The quantum effects encapsulated in loop corrections are crucial in quantum field theory for a wide variety of formal and phenomenological applications. In this article we propose and check a definition of the so-called single cut…
We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the…
We calculate the one-loop quantum corrections in the cubic Galileon theory, using cutoff regularization. We confirm the expected form of the one-loop effective action and that the couplings of the Galileon theory do not get renormalized.…
We give an explicit proof that the noncommutative U(N) gauge theories are one-loop renormalizable
We calculate the one-loop perturbative correction to the coefficient of the \cs term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual $U(1)$ symmetry,…
An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…
What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry \`a la Connes, deliberately unveiling the answers to these questions.…
This paper studies the spectrum of a multi-dimensional split-step quantum walk with a defect that cannot be analysed in the previous papers. To this end, we have developed a new technique which allow us to use a spectral mapping theorem for…
In the past few years, the unifying frameworks of 4-dimensional Chern-Simons theory and affine Gaudin models have allowed for the systematic construction of a large family of integrable $\sigma$-models. These models depend on the data of a…
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis…
We study for the first time the effect of the geometry of quantum wire networks on their nonlinear optical properties and show that for some geometries, the first hyperpolarizability is largely enhanced and the second hyperpolarizability is…
We adopt a novel approach to combine path integral methods with Loop Quantum Gravity (LQG). Our approach builds upon the recently developed coherent state path integral formulation of LQG to compute the one-loop effective action. We compare…
We derive the quantum effective action up to second order in gradients and up to two-loop order for an interacting scalar field theory. This expansion of the effective action is useful to study problems in cosmological settings where…
We derive the expressions for the 1-loop corrections in cosmological, Eulerian, perturbation theory to the matter bispectrum and to the galaxy bispectrum, assuming local galaxy bias, in presence of non-Gaussian initial conditions. We…