Path integral quantization of scalar fluctuations above a kink

We quantize scalar fluctuations in 1+1 dimensions above a classical background kink. The properties of the effective action for the corresponding classical field are studied with an exact functional method, alternative to exact Wilsonian renormalization, where the running parameter is a bare mass, and the regulator of the quantum theory is fixed. We extend this approach, in an appendix, to a Yukawa interaction in higher dimension.Comment: Comments adde

On higher-order corrections in a four-fermion Lifshitz model

We study a flavour-violating four-fermion interaction in the Lifshitz context, in 3+1 dimensions and with a critical exponent z=3. This model is renormalizable, and features dynamical mass generation, as well as asymptotic freedom. At one-loop, it is only logarithmically divergent, but the superficial degree of divergence of the two-point functions is 3. We calculate the two-loop corrections to the propagators, and show that, at this order, the Lorentz-violating corrections to the IR dispersion relation are quadratic in the cut off. Furthermore, these corrections are too important to represent a physical effect. As a consequence, the predictive power of the model in terms of Lorentz-violating effects in the propagation of particles is limited.Comment: 20 pages, 3 figures, comments adde

Non-Perturbative Formulation of Time-Dependent String Solutions

We formulate here a new world-sheet renormalization-group technique for the bosonic string, which is non-perturbative in the Regge slope alpha' and based on a functional method for controlling the quantum fluctuations, whose magnitudes are scaled by the value of alpha'. Using this technique we exhibit, in addition to the well-known linear-dilaton cosmology, a new, non-perturbative time-dependent background solution. Using the reparametrization invariance of the string S-matrix, we demonstrate that this solution is conformally invariant to alpha', and we give a heuristic inductive argument that conformal invariance can be maintained to all orders in alpha'. This new time-dependent string solution may be applicable to primordial cosmology or to the exit from linear-dilaton cosmology at large times

Quantization leading to a natural flattening of the axion potential

Starting from the general cosine form for the axion effective potential, we quantize the axion and show that the result is described by a naturally flat potential, if interactions with other particles are not considered. This feature therefore restores the would-be Goldstone-boson nature of the axion, and we calculate the corresponding vacuum energy density, which does not need to be too large by orders of magnitude compared to Dark Energy

Functional Callan-Symanzik equation for QED

An exact evolution equation, the functional generalization of the Callan-Symanzik method, is given for the effective action of QED where the electron mass is used to turn the quantum fluctuations on gradually. The usual renormalization group equations are recovered in the leading order but no Landau pole appears.Comment: 9 pages, no figure

Control of quantum fluctuations for a Yukawa interaction in the Kaluza Klein picture

We study a system of fermions interacting with a scalar field, in 4+1 dimensions where the 5th dimension is compactified, using an exact functional method, where quantum fluctuations are controlled by the amplitude of the bare fermion mass. The integration of our equationsleads to the properties of the dressed Yukawa coupling, that we study at one-loop so as to show the consistency of the approach. Beyond one loop, the non-perturbative aspect of the method gives us the possibility to derive the dynamical fermion mass. The result obtained is cut off independent and this derivation proposes an alternative to the Schwinger-Dyson approach.Comment: extended discussion on the scalar effective potentia