Searcharxiv⌕ Search

arXiv subjects

E. M. Santangelo

Publications and source records attributed to E. M. Santangelo.

36 records · Page 2Linked to original sources
arXiv2004

Finite temperature properties of the Dirac operator under local boundary conditions

We study the finite temperature free energy and fermion number for Dirac fields in a one-dimensional spatial segment, under two different members of the family of local boundary conditions defining a self-adjoint Euclidean Dirac operator in two dimensions. For one of such boundary conditions, compatible with the presence of a spectral asymmetry, we discuss in detail the contribution of this part of the spectrum to the zeta-regularized determinant of the Dirac operator and, thus, to the finite temperature properties of the theory.

hep-th↗
arXiv2004

Spectral functions of the Dirac operator under local boundary conditions

After a brief discussion of elliptic boundary problems and their properties, we concentrate on a particular example: the Euclidean Dirac operator in two dimensions, with its domain determined by local boundary conditions. We discuss the meromorphic structure of the zeta function of the associated second order problem, as well as the main characteristic of the first order problem, i.e., the boundary contribution to the spectral asymmetry, as defined through the eta function.

hep-th↗
arXiv2002

Spectral asymmetry for bag boundary conditions

We give an expression, in terms of boundary spectral functions, for the spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its domain is determined by local boundary conditions, and the manifold is of product type. As an application, we explicitly evaluate the asymmetry in the case of a finite-length cylinder, and check that the outcome is consistent with our general result. Finally, we study the asymmetry in a disk, which is a non-product case, and propose an interpretation.

hep-th↗
arXiv2001

Boundary dynamics and multiple reflection expansion for Robin boundary conditions

In the presence of a boundary interaction, Neumann boundary conditions should be modified to contain a function S of the boundary fields: (\nabla_N +S)ϕ=0. Information on quantum boundary dynamics is then encoded in the $S$-dependent part of the effective action. In the present paper we extend the multiple reflection expansion method to the Robin boundary conditions mentioned above, and calculate the heat kernel and the effective action (i) for constant S, (ii) to the order S^2 with an arbitrary number of tangential derivatives. Some applications to symmetry breaking effects, tachyon condensation and brane world are briefly discussed.

hep-th↗
arXiv2001

Evaluation of Casimir energies through spectral functions

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 emphasized, and the renormalization issue is discussed through simple examples.

hep-th↗
arXiv2001

Multiple reflection expansion and heat kernel coefficients

We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the coefficients for Dirichlet and Neumann boundary conditions. Further, we calculate the heat kernel coefficients for the most general matching conditions on the surface of a sphere, including those cases corresponding to the presence of delta and delta prime background potentials. In the latter case, the multiple reflection expansion is shown to be non-convergent.

hep-th↗
arXiv2001

Effective action for QED_4 through zeta function regularization

We obtain, through zeta function methods, the one-loop effective action for massive Dirac fields in the presence of a uniform, but otherwise general, electromagnetic background. After discussing renormalization, we compare our zeta function result with Schwinger's proper time approach.

hep-th↗
arXiv1999

Casimir energy of massive MIT fermions in a Bohm-Aharonov background

We study the effect of a background flux string on the vacuum energy of massive Dirac fermions in 2+1 dimensions confined to a finite spatial region through MIT boundary conditions. We treat two admissible self-adjoint extensions of the Hamiltonian and compare the results. In particular, for one of these extensions, the Casimir energy turns out to be discontinuous at integer values of the flux.

hep-th↗
arXiv1999

Dirac fields in the background of a magnetic flux string and spectral boundary conditions

We study the problem of a Dirac field in the background of an Aharonov-Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behaviour of eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency with the index theorem, and evaluate its vacuum fermionic number and Casimir energy.

hep-th↗
arXiv1998

Dirac fields in a Bohm-Aharonov background and spectral boundary conditions

We study the problem of a Dirac field in the background of an Aharonov-Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behaviour of the eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency with the index theorem, and discuss the vacuum fermionic number and Casimir energy.

hep-th↗
arXiv1996

Dirac Operator on a disk with global boundary conditions

We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the connection between our result and the index theorem.

hep-th↗
arXiv1996

Determinants of Dirac operators with local boundary conditions

We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to the case of a bidimensional disk under bag-like conditions.

hep-th↗
arXiv1995

Cheshire Cat Scenario in a 3+1 dimensional Hybrid Chiral Bag

The total energy in the two-phase chiral bag model is studied, including the contribution due to the bag (Casimir energy plus energy of the valence quarks), as well as the one coming from the Skyrmion in the external sector. A consistent determination of the parameters of the model and the renormalization constants in the energy is performed. The total energy shows an approximate independence with the bag radius (separation limit between the phases), in agreement with the Cheshire Cat Principle.

hep-ph↗
arXiv1995

Connection between $ζ$ and cutoff regularizations of Casimir energies

We study the connection between $ζ$- and cutoff-regularized Casimir energies for scalar fields. We show that, in general, both regularization schemes lead to divergent contributions, and to finite parts which do not coincide. We determine the relationships among the various coefficients appearing in one approach and the other. As an application, we discuss the case of scalar fields in $d$-dimensional boxes under periodic boundary conditions.

hep-th↗
arXiv1994

Confined two-dimensional fermions at finite density

We introduce the chemical potential in a system of two-dimensional massless fermions, confined to a finite region, by imposing twisted boundary conditions in the Euclidean time direction. We explore in this simple model the application of functional techniques which could be used in more complicated situations.

hep-th↗
arXiv1994

Determinants of elliptic boundary problems for Dirac operators I. Local boundary conditions

We study functional determinants for Dirac operators on manifolds with boundary and discuss the ellipticity of boundary problems by using the Calderón projector. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to the case of a bidimensional disk under bag-like conditions.

funct-an↗
arXiv1993

A calculation with a bi-orthogonal wavelet transformation

We explore the use of bi-orthogonal basis for continuous wavelet transformations, thus relaxing the so-called admissibility condition on the analyzing wavelet. As an application, we determine the eigenvalues and corresponding radial eigenfunctions of the Hamiltonian of relativistic Hydrogen-like atoms.

funct-an↗