Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras

$C^*$-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutative twisted Banach-$*$-algebras on the stage of measures on the not locally compact test function space. Already within this frame strict deformation quantization is obtained, but in terms of Banach-$*$-algebras instead of $C^*$-algebras. Fourier transformation and representation theory of the measure Banach-$*$-algebras are combined with the theory of continuous projective group representations to arrive at the genuine $C^*$-algebraic strict deformation quantization in the sense of Rieffel and Landsman. Weyl quantization is recognized to depend in the first step functorially on the (in general) infinite dimensional, pre-symplectic test function space; but in the second step one has to select a family of representations, indexed by the deformation parameter $\hbar$. The latter ambiguity is in the present investigation connected with the choice of a folium of states, a structure, which does not necessarily require a Hilbert space representation.Comment: This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras

C*-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutative twisted Banach-*-algebras on the stage of measures on the not locally compact test function space. Already within this frame strict deformation quantization is obtained, but in terms of Banach-*-algebras instead of C*-algebras. Fourier transformation and representation theory of the measure Banach-*-algebras are combined with the theory of continuous projective group representations to arrive at the genuine C*-algebraic strict deformation quantization in the sense of Rieffel and Landsman. Weyl quantization is recognized to depend in the first step functorially on the (in general) infinite dimensional, pre-symplectic test function space; but in the second step one has to select a family of representations, indexed by the deformation parameter h. The latter ambiguity is in the present investigation connected with the choice of a folium of states, a structure, which does not necessarily require a Hilbert space representation

Interrelations between Stochastic Equations for Systems with Pair Interactions

Several types of stochastic equations are important in thermodynamics, chemistry, evolutionary biology, population dynamics and quantitative social science. For systems with pair interactions four different types of equations are derived, starting from a master equation for the state space: First, general mean value and (co)variance equations. Second, Boltzmann-like equations. Third, a master equation for the configuration space allowing transition rates which depend on the occupation numbers of the states. Fourth, a Fokker-Planck equation and a ``Boltzmann-Fokker-Planck equation''. The interrelations of these equations and the conditions for their validity are worked out clearly. A procedure for a selfconsistent solution of the nonlinear equations is proposed. Generalizations to interactions between an arbitrary number of systems are discussed.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermion and Quantum Spins

We study the macroscopic dynamics of fermion and quantum-spin systems with long-range, or mean-field, interactions, which turns out to be equivalent to an intricate combination of classical and short-range quantum dynamics. In this paper we focus on the quantumpart of the long-range macroscopic dynamics. The classical part is studied in a companion paper. Altogether, the results obtained are far beyond previous ones and required the development of a suitable mathematical framework. The entanglement of classical and quantum worlds is noteworthy, opening new theoretical perspectives, and is shown here to be a consequence of the highly non-local character of long-range, or mean-field, interactions.CNPq (308337/2017-4), FAPESP (2017/22340-9), Basque Government through the grant IT641-13 MTM2017-82160-C2-2-

Gas-kinetic derivation of Navier-Stokes-like traffic equations

Macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies. Therefore, this paper shows how to construct a logically consistent fluid-dynamic traffic model from basic laws for the acceleration and interaction of vehicles. These considerations lead to the gas-kinetic traffic equation of Paveri-Fontana. Its stationary and spatially homogeneous solution implies equilibrium relations for the `fundamental diagram', the variance-density relation, and other quantities which are partly difficult to determine empirically. Paveri-Fontana's traffic equation allows the derivation of macroscopic moment equations which build a system of non-closed equations. This system can be closed by the well proved method of Chapman and Enskog which leads to Euler-like traffic equations in zeroth-order approximation and to Navier-Stokes-like traffic equations in first-order approximation. The latter are finally corrected for the finite space requirements of vehicles. It is shown that the resulting model is able to withstand the above mentioned criticism.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Photons in Fock space and beyond

The three-volume major reference "Photons in Fock Space and Beyond" undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame. The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise. A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional "cohomological fields" explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems

Passive security analysis of current TLS implementations and configurations in the eduroam EAP-TLS environment

The eduroam network connects institutions using the protocols RADIUS and EAP to ensure a personalized login into the network while keeping the separation between Identity Providers (IdP), which hold account information, and Service Providers (SP), which provide Internet access. To ensure the privacy of the users and to keep the credentials secret from the visited institutions, the login has to be encrypted. Most EAP methods use the well-known security protocol Transport Layer Security (TLS) to achive this. The most commonly used EAP methods are TTLS (Tunneled TLS) and PEAP (Protected EAP), which both rely on EAP-TLS. EAP-TLS specifies the usage of TLS inside EAP. Like for most other federated networks, where the members have to trust each other, the security of the whole network depends on the security of the weakest link. In EAP-TLS, there are two relevant classes of devices for the security analysis: The supplicants (acting as TLS clients) and the authentication servers (acting as TLS servers). This thesis gives an overview of the current operational practices in the usage of TLS in EAP-TLS and aims to determine if security problems exist. This is achieved by a passive analysis of the EAP and TLS handshake messages exchanged in the process of the eduroam login. By passively analyzing the traffic, one can learn about the capabilities of the client, since the client sends its capabilities in the Client Hello message of the TLS handshake. The server on the other hand reacts on the Client Hello. To assess the server fully, one has to simulate different clients and capture the corresponding answer. Since this thesis focuses on a passive analysis, it deals with the current status of client implementations and configurations. The reaction of the servers is captured and analyzed, but the complete analysis of the servers will be part of a future work