Calculation of Ground State Energy for Confined Fermion Fields

A method for renormalization of the Casimir energy of confined fermion fields in (1+1)D is proposed. It is based on the extraction of singularities which appear as poles at the point of physical value of the regularization parameter, and subsequent compensation of them by means of redefinition of the "bare" constants. A finite ground state energy of the two-phase hybrid model of fermion bag with chiral boson-fermion interaction is calculated as the function of the bag's size.Comment: 10 pages, LaTeX; no figures. Version to appear in Phys. Lett. B (2001

Chiral Hybrid Bag Model with the Boson Field inside the Bag

The three-phase version of the hybrid chiral bag model, containing the phase of asymptotic freedom, the hadronization phase as well as the intermediate phase of constituent quarks, is proposed. For this model the self-consistent solution, which takes into account the fermion vacuum polarization effects, is found in (1+1) D. Within this solution the total energy of the bag, including the one-loop contribution from the Dirac's sea, is studied as the function of the bag geometry under condition of nonvanishing boson condensate density in the interior region. The existence and uniqueness of the ground state bag configuration, which minimizes the total energy and contains all the three phases, are shown.Comment: 17 text pages, 3 figure

Quantum Field Theories on Manifolds with Curved Boundaries: Scalar Fields

A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed Dirichlet and Neumann boundary conditions. The method is applied to a general renormalisable scalar field theory in four dimensions using dimensional regularisation to two loops and expanding about arbitrary background fields. Detailed results are also specialised to an $O(n)$ symmetric model with a single coupling constant. Extra boundary terms are introduced into the action which give rise to either Dirichlet or generalised Neumann boundary conditions for the quantum fields. For plane boundaries the resulting renormalisation group functions are in accord with earlier results but here the additional terms depending on the extrinsic curvature of the boundary are found. Various consistency relations are also checked and the implications of conformal invariance at the critical point where the $\beta$ function vanishes are also derived. The local Scr\"odinger equation for the wave functional defined by the functional integral under deformations of the boundary is also verified to two loops. Its consistency with the renormalisation group to all orders in perturbation theory is discussed.Comment: 50 pages, DAMTP/92-3