Belinfante Tensors Induced by Matter-Gravity Couplings

We show that any generally covariant coupling of matter fields to gravity gives rise to a conserved, on-shell symmetric energy-momentum tensor equivalent to the canonical energy-momentum tensor of the flat-space theory. For matter fields minimally coupled to gravity our algorithm gives the conventional Belinfante tensor. We establish that different matter-gravity couplings give metric energy-momentum tensors differing by identically conserved tensors. We prove that the metric energy-momentum tensor obtained from an arbitrary gravity theory is on-shell equivalent to the canonical energy-momentum tensor of the flat-space theory.Comment: 10 pages, LaTex; misprints corrected, references added; to appear in Physical Review

Experiences with formal engineering: model-based specification, implementation and testing of a software bus at Neopost

We report on the actual industrial use of formal methods during the development of a software bus. During an internship at Neopost Inc., of 14 weeks, we developed the server component of a software bus, called the XBus, using formal methods during the design, validation and testing phase: we modeled our design of the XBus in the process algebra mCRL2, validated the design using the mCRL2-simulator, and fully automatically tested our implementation with the model-based test tool JTorX. This resulted in a well- tested software bus with a maintainable architecture. Writing the model (mdev), simulating it, and testing the implementation with JTorX only took 17% of the total development time. Moreover, the errors found with model-based testing would have been hard to find with conventional test methods. Thus, we show that formal engineering can be feasible, beneficial and cost-effective.\ud The findings above, reported earlier by us in (Sijtema et al., 2011) [1], were well- received, also in industrially oriented conferences (Ferreira and Romanenko, 2010) [2] and [3]. In this paper, we look back on the case study, and carefully analyze its merits and shortcomings. We reflect on (1) the added benefits of model checking, (2) model completeness and (3) the quality and performance of the test process.\ud Thus, in a second phase, after the internship, we model checked the XBus protocol—this was not done in [1] since the Neopost business process required a working implementation after 14 weeks. We used the CADP tool evaluator4 to check the behavioral requirements obtained during the development. Model checking did not uncover errors in model mdev, but revealed that model mdev was neither complete nor optimized: in particular, requirements to the so-called bad weather behavior (exceptions, unexpected inputs, etc.) were missing. Therefore, we created several improved models, checked that we could validate them, and used them to analyze quality and performance of the test process. Model checking was expensive: it took us approx. 4 weeks in total, compared to 3 weeks for the entire model-based testing approach during the internship.\ud In the second phase, we analyzed the quality and performance of the test process, where we looked at both code and model coverage. We found that high code coverage (almost 100%) is in most cases obtained within 1000 test steps and 2 minutes, which matches the fact that the faults in the XBus were discovered within a few minutes.\ud Summarizing, we firmly believe that the formal engineering approach is cost-effective, and produces high quality software products. Model checking does yield significantly better models, but is also costly. Thus, system developers should trade off higher model quality against higher costs

Correlation functions, Bell's inequalities and the fundamental conservation laws

I derive the correlation function for a general theory of two-valued spin variables that satisfy the fundamental conservation law of angular momentum. The unique theory-independent correlation function is identical to the quantum mechanical correlation function. I prove that any theory of correlations of such discrete variables satisfying the fundamental conservation law of angular momentum violates the Bell's inequalities. Taken together with the Bell's theorem, this result has far reaching implications. No theory satisfying Einstein locality, reality in the EPR-Bell sense, and the validity of the conservation law can be constructed. Therefore, all local hidden variable theories are incompatible with fundamental symmetries and conservation laws. Bell's inequalities can be obeyed only by violating a conservation law. The implications for experiments on Bell's inequalities are obvious. The result provides new insight regarding entanglement, and its measures.Comment: LaTeX, 12pt, 11 pages, 2 figure

Dynamics of a self gravitating light-like matter shell: a gauge-invariant Lagrangian and Hamiltonian description

A complete Lagrangian and Hamiltonian description of the theory of self-gravitating light-like matter shells is given in terms of gauge-independent geometric quantities. For this purpose the notion of an extrinsic curvature for a null-like hypersurface is discussed and the corresponding Gauss-Codazzi equations are proved. These equations imply Bianchi identities for spacetimes with null-like, singular curvature. Energy-momentum tensor-density of a light-like matter shell is unambiguously defined in terms of an invariant matter Lagrangian density. Noether identity and Belinfante-Rosenfeld theorem for such a tensor-density are proved. Finally, the Hamiltonian dynamics of the interacting system: ``gravity + matter'' is derived from the total Lagrangian, the latter being an invariant scalar density.Comment: 20 pages, RevTeX4, no figure

A test generation framework for quiescent real-time systems

We present an extension of Tretmans theory and algorithm for test generation for input-output transition systems to real-time systems. Our treatment is based on an operational interpretation of the notion of quiescence in the context of real-time behaviour. This gives rise to a family of implementation relations parameterized by observation durations for quiescence. We define a nondeterministic (parameterized) test generation algorithm that generates test cases that are sound with respect to the corresponding implementation relation. Also, the test generation is exhaustive in the sense that for each non-conforming implementation a test case can be generated that detects the non-conformance

Optimal Control of Quantum Dynamics : A New Theoretical Approach

A New theoretical formalism for the optimal quantum control has been presented. The approach stems from the consideration of describing the time-dependent quantum system in terms of the real physical observables, viz., the probability density rho(x,t) and the quantum current j(x,t) which is well documented in the Bohm's hydrodynamical formulation of quantum mechanics. The approach has been applied for manipulating the vibrational motion of HBr in its ground electronic state under an external electric field.Comment: 4 figure

Reality, measurement and locality in Quantum Field Theory

It is currently believed that the local causality of Quantum Field Theory (QFT) is destroyed by the measurement process. This belief is also based on the Einstein-Podolsky-Rosen (EPR) paradox and on the so-called Bell's theorem, that are thought to prove the existence of a mysterious, instantaneous action between distant measurements. However, I have shown recently that the EPR argument is removed, in an interpretation-independent way, by taking into account the fact that the Standard Model of Particle Physics prevents the production of entangled states with a definite number of particles. This result is used here to argue in favor of a statistical interpretation of QFT and to show that it allows for a full reconciliation with locality and causality. Within such an interpretation, as Ballentine and Jarret pointed out long ago, Bell's theorem does not demonstrate any nonlocality.Comment: 15 pages. Published versio

Covariant Linear Response Theory of Relativistic QED Plasmas

We start from the QED Lagrangian to describe a charged many-particle system coupled to the radiation field. A covariant density matrix approach to kinetic theory of QED plasmas, subjected to a strong external electro-magnetic field has recently been developed [1,2]. We use the hyperplane formalism in order to perform a manifest covariant quantization and to implement initial correlations to the solution of the Liouville-von Neumann equation. A perturbative expansion in orders of the fine structure constant for the correlation functions as well as the statistical operator is applied. The non-equilibrium state of the system is given within generalized linear response theory. Expressions for the susceptibility tensor, describing the plasma response, are calculated within different approximations, like the RPA approximation or considering collisions within the Born-approximation. In particular, the process of relativistic inverse bremsstrahlung in a plasma is discussed.Comment: Latex 39 pages, 4 figure