Related papers: Justification of the zeta function renormalization…
The Casimir energy of a non-uniform string built up from two pieces with different speed of sound is calculated. A standard procedure of subtracting the energy of an infinite uniform string is applied, the subtraction being interpreted as…
The main part of this paper is to present an updated review of the Casimir energy at zero and finite temperature for the transverse oscillations of a piecewise uniform closed string. We make use of three different regularizations: the…
In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials is analyzed. It is shown that the energy contains contributions which…
The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. The great adaptibility of this string model with respect to various regularization methods is pointed out. We survey several…
This is an introductory set of lectures on elliptic differential operators and boundary problems, and their associated spectral functions. The role of zeta functions and traces of heat kernels in the regularization of Casimir energies is…
Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using zeta function regularization methods, the results are analytically continued and…
The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. The string consists of 2N pieces of equal length, of alternating type I and type II material, and is taken to be relativistic in the…
A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at…
We compare two renormalization procedures, one based on the short distance behavior of heavy quark-antiquark free energies and the other by using bare Polyakov loops at different temporal extent of the lattice and find that both…
We regard the Wheeler-De Witt equation as a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The used method to study such a problem is a variational approach with Gaussian trial wave…
The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. The great adaptability of this string model with respect to various regularization methods is pointed out. We survey several…
The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. The string is relativistic in the sense that the velocity of transverse waves is always equal to c. The great adaptibility of this string…
Using the fact that a finite sum of power series are given by the difference between two zeta functions, we justify the usage of the zeta function with a negative variable in physical problems to avoid the divergence of the infinite sum. We…
We propose a procedure for the renormalization of Casimir energy, that is based on the implicit versions of standard steps of renormalization procedure --- regularization, subtraction and removing the regularization. The proposed procedure…
A non-subtractive recipe of Casimir energy renormalization efficient in the presence of logarithmically divergent terms is proposed. It is demonstrated that it can be applied even then, when energy levels can be obtained only numerically…
We introduce a D-dimensional Hamiltonian formalism for the study of Polyakov loop models of finite temperature gauge theories in D+1 dimensions. Polyakov loop string tensions are obtained from energy eigenstates of the Hamiltonian. For D=1,…
We study classically unstable string type configurations and compute the renormalized vacuum polarization energies that arise from fermion fluctuations in a 2+1 dimensional analog of the standard model. We then search for a minimum of the…
We review some recent results on the calculation of renormalization constants in Yang-Mills theory using open bosonic strings. The technology of string amplitudes, supplemented with an appropriate continuation off the mass shell, can be…
We consider an open string with ends laying on the two different solid beams (rods). This set-up is equivalent to two scalar fields with a set of constraints at their end-points. We calculate the zero-point energy and the Casimir energy in…
In this work we attempt to show in a clear and simple manner the fundamental ideas of the Renormalization Theory. With that intention we use two well-known problems of the Physic and Engeneering undergraduate students, the calculation of…