W. Garcia Fuertes

Generalized zeta functions and one-loop corrections to quantum kink masses

Abstract A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two P ( φ ) 2 systems with polynomial self-interactions.

One-loop corrections to classical masses of kink families

Abstract One-loop corrections to kink masses in a family of (1+1)-dimensional field theoretical models with two real scalar fields are computed. A generalized DHN formula applicable to potentials with and without reflection is obtained. It is shown how half-bound states arising in the spectrum of the second-order fluctuation operator for one-component topological kinks and the vacuum play a central role in the computation of the kink Casimir energy. The issue of whether or not the kink degeneracy exhibited by this family of models at the classical level survives one-loop quantum fluctuations is addressed.

Semi-classical mass of quantum k-component topological kinks

Abstract We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the TK1 and TK2 kinks in a deformation of the O ( N ) linear sigma model on the real line.

Quantum oscillations of self-dual Abrikosov-Nielsen-Olesen vortices

The mass shift induced by one-loop quantum fluctuations on self-dual Abrikosov-Nielsen-Olesen (ANO) vortices is computed using heat kernel/generalized zeta function regularization methods. The quantum masses of superimposed multivortices with vorticity lower than five are given. The case of two separate vortices with a quantum of magnetic flux is also discussed.

One-loop corrections to the mass of self-dual semi-local planar topological solitons

Abstract A formula is derived that allows the computation of one-loop mass shifts for self-dual semilocal topological solitons. These extended objects, which in three spatial dimensions are called semi-local strings, arise in a generalized Abelian Higgs model with a doublet of complex Higgs fields. Having a mixture of global, SU ( 2 ) , and local (gauge), U ( 1 ) , symmetries, this weird system may seem bizarre, but it is in fact the bosonic sector of electro-weak theory when the weak mixing angle is π 2 . The procedure for computing the semi-classical mass shifts is based on canonical quantization and heat kernel/zeta function regularization methods.

A perturbative approach to the quantum elliptic Calogero-Sutherland model

Abstract We solve perturbatively the quantum elliptic Calogero–Sutherland model in the regime in which the quotient between the real and imaginary semiperiods of the Weierstrass P function is small.

Two species of vortices in massive gauged non-linear sigma models

A bstractNon-linear sigma models with scalar fields taking values on ℂℙn

DERIVATIVES OF GENERALIZED GEGENBAUER POLYNOMIALS

\mathbb{C}{\mathrm{\mathbb{P}}}^n