J. E. Solomin

Chiral symmetry and functional integral

Abstract The change in the fermionic functional integral measure under chiral rotations is analyzed. Using the ζ-function method, the evaluation of chiral Jacobians to theories including nonhermitian Dirac operators D , can be extended in a natural way. (This being of interest, for example, in connection with the Weinberg-Salam model or with the relativistic string theory.) Results are compared with those obtained following other approaches, the possible discrepancies are analyzed and the equivalence of the different methods under certain conditions on D is proved. Also shown is how to compute the Jacobian for the case of a finite chiral transformation and this result is used to develop a sort of path-integral version of bosonization in d = 2 space-time dimensions. This result is used to solve in a very simple and economical way relevant d = 2 fermionic models. Furthermore, some interesting features in connection with the θ-vacuum in d = 2,4 gauge theories are discussed.

Path Integral Formulation of Two-dimensional Gauge Theories With Massless Fermions

Abstract We study (1 + 1) dimensional gauge theories [with SU( N ) and diagonal SU( N ) color symmetry] using the functional integral method. We construct an effective lagrangian by performing a change in the fermionic variables, and then investigate relevant phenomena such as the intrinsic Higgs mechanism and color screening.

Finite Element Analysis of a Quadratic Eigenvalue Problem Arising in Dissipative Acoustics

A quadratic eigenvalue problem arising in the determination of the vibration modes of an acoustic fluid contained in a cavity with absorbing walls is considered. The problem is shown to be equivalent to the spectral problem for a noncompact operator and a thorough spectral characterization is given. A numerical discretization based on Raviart--Thomas finite elements is analyzed. The method is proved to be free of spurious modes and to converge with optimal order. Implementation issues and numerical experiments confirming the theoretical results are reported.

Approximation of the vibration modes of a plate by Reissner-Mindlin equations

This paper deals with the approximation of the vibration modes of a plate modelled by the Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is the mixed interpolation tensorial components, based on the family of elements called MITC. We use the lowest order method of this family. Applying a general approximation theory for spectral problems, we obtain optimal order error estimates for the eigenvectors and the eigenvalues. Under mild assumptions, these estimates are valid with constants independent of the plate thickness. The optimal double order for the eigenvalues is derived from a corresponding L 2 -estimate for a load problem which is proven here. This optimal order L 2 -estimate is of interest in itself. Finally, we present several numerical examples showing the very good behavior of the numerical procedure even in some cases not covered by our theory.

Finite element analysis of the vibration problem of a plate coupled with a fluid

Summary. We consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid. The plate is modelled by Reissner-Mindlin equations while the fluid is described in terms of displacement variables. This formulation leads to a symmetric eigenvalue problem. Reissner-Mindlin equations are discretized by a mixed method, the equations for the fluid with Raviart-Thomas elements and a non conforming coupling is used on the interface. In order to prove that the method is locking free we consider a family of problems, one for each thickness

ζ‐function method and the evaluation of fermion currents

t>0

Determinants of Dirac operators with local boundary conditions

, and introduce appropriate scalings for the physical parameters so that these problems attain a limit when

A calculation with a biorthogonal wavelet transformation

t\to 0

On Chiral Rotations and the Fermionic Path Integral

. We prove that spurious eigenvalues do not arise with this discretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t. Finally we present numerical results confirming the good performance of the method.

On the global version of Euler–Lagrange equations

Using the ζ‐function method, a prescription for the evaluation of fermion currents in the presence of background fields is given. The method preserves gauge invariance at each step of the computation and yields to a finite answer showing the relevant physical properties for arbitrary background configurations. Examples for n=2,3 dimensions are worked out, emphasizing the connection between preservation of gauge invariance and violation of other symmetries (chiral symmetry for n=2, parity for n=3).