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We report on preliminary results on the measurement of variations of the Casimir energy in rigid cavities through its influence on the superconducting transition of in-cavity aluminium (Al) thin films. After a description of the experimental apparatus we report on a measurement made with thermal photons, discussing its implications for the zero-point photons case. Finally we show the preliminary results for the zero-point case., Comment: 9 pages, 7 figures, Talk given at QFEXT07 Conference in Liepzig: Quantum Field Theory Under the Influence of External Conditions

Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the supporting manifold (compactified spacetime or spatial slice) interpreting it as a finite topological approximation in the sense of Sorkin. This finite space is entirely described by the algebra of cochains with the cup product. The methods of Connes and Lott are then used to develop gauge theories on this algebra and to derive Wilson's actions for the gauge and Dirac fields therefrom which can now be given geometrical meaning. We also describe very natural candidates for the QCD theta term and Chern-Simons action suggested by this algebraic formulation. Some of these formulations are simpler than currently available alternatives. The paper treats both the functional integral and Hamiltonian approaches., Comment: 34 pages, Latex, Minor corrections, Section 6 corrected

Lattice discretizations of continuous manifolds are common tools used in a variety of physical contexts. Conventional discrete approximations, however, cannot capture all aspects of the original manifold, notably its topology. In this paper we discuss an approximation scheme due to Sorkin which correctly reproduces important topological aspects of continuum physics. The approximating topological spaces are partially ordered sets (posets), the partial order encoding the topology. Now, the topology of a manifold $M$ can be reconstructed from the commutative C*-algebra $\cc(M)$ of continuous functions defined on it. In turn, this algebra is generated by continuous probability densities in ordinary quantum physics on $M$. The latter also serve to specify the domains of observables like the Hamiltonian. For a poset, the role of this algebra is assumed by a noncommutative C$^*$-algebra $\ca $. This fact makes any poset a genuine `noncommutative' (`quantum') space, in the sense that the algebra of its `continuous functions' is a noncommutative C$^*$-algebra. We therefore also have a remarkable connection between finite approximations to quantum physics and noncommutative geometries. We use this connection to develop various approximation methods for doing quantum physics using $\ca$.