Finite temperature properties of the Dirac operator with bag boundary conditions

We study the finite temperature free energy and fermion number for Dirac fields in a one-dimensional spatial segment, under local boundary conditions compatible with the presence of a spectral asymmetry. We discuss in detail the contribution of this part of the spectrum to the determinant. We evaluate the finite temperature properties of the theory for arbitrary values of the chemical potential.Comment: Talk given at the Seventh International Workshop Quantum Field Theory under the influence of External Conditions, QFEXT'05, Barcelona, Spain. Final version, to appear in Journal of Physics A: Mathematical and Genera

Spectral action for torsion with and without boundaries

We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues of the previous calculations, show that many terms in fact cancel out, and demonstrate that this cancellation is a result of the chiral symmetry of spectral action. On the boundary, we calculate several leading terms in the expansion of spectral action in four dimensions for vanishing chiral parameter $\theta$ of the boundary conditions, and show that $\theta=0$ is a critical point of the action in any dimension and at all orders of the expansion.Comment: 16 pages, references adde