There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.

According to the introduction of a minimal length to quantum field theory which is directly related to a generalized uncertainty principle the implementation of the gauge principle becomes much more intricated. It has been shown in another paper how gauge theories have to be extended in general, if there is assumed the existence of a minimal length. In this paper this generalization of the description of gauge theories is applied to the case of Yang-Mills theories with gauge group SU (N ) to consider especially the application to the electroweak theory as it appears in the standard model. The modifications of the lepton-, Higgs-and gauge field sector of the extended Lagrangian of the electroweak theory maintaining local gauge invariance under SU (2)L ⊗ U (1)Y transformations are investigated. There appear additional interaction terms between the leptons or the Higgs particle respectively with the photon and the W-and Z-bosons as well as additional self-interaction terms of these gauge bosons themselves. It is remarkable that in the quark sector where the full gauge group of the standard model, SU (3)c ⊗ SU (2)L ⊗ U (1)Y , has to be considered there arise coupling terms between the gluons und the W-and Z-bosons which means that the electroweak theory is not separated from quantum chromodynamics anymore.

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to Noncommutative Geometry. We explore, as toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime. Then we investigate the more realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative planes. As a result, we obtain propagators, which are finite in the ultraviolet as well as the infrared regime.

We calculate the inclusive cross section of double Z-boson production within large extra dimensions at the Large Hadron Collider (LHC). Using perturbatively quantized gravity in the ADD model we perform a first order calculation of the graviton mediated contribution to the pp → ZZ + x cross section. At low energies (e.g. Tevatron) this additional contribution is very small, making it virtually unobservable, for a fundamental mass scale above 2500 GeV. At LHC energies however, the calculation indicates that the ZZ-production rate within the ADD model should differ significantly from the Standard Model if the new fundamental mass scale would be below 15000 GeV. A comparison with the observed production rate at the LHC might therefore provide direct hints on the number and structure of the extra dimensions.

In this paper, a generalized quantization principle for the gravitational field in canonical quantum gravity, especially with respect to quantum geometrodynamics is considered. This assumption can be interpreted as a transfer from the generalized uncertainty principle in quantum mechanics, which is postulated as generalization of the Heisenberg algebra to introduce a minimal length, to a corresponding quantization principle concerning the quantities of quantum gravity. According to this presupposition there have to be given generalized representations of the operators referring to the observables in the canonical approach of a quantum description of general relativity. This also leads to generalized constraints for the states and thus to a generalized Wheeler-DeWitt equation determining a new dynamical behavior. As a special manifestation of this modified canonical theory of quantum gravity, quantum cosmology is explored. The generalized cosmological Wheeler-DeWitt equation corresponding to the application of the generalized quantization principle to the cosmological degree of freedom is solved by using Sommerfelds polynomial method.

One of the major challenges of the future automotive development is to achieve the required reductions of the CO 2 emissions. Therefore, it is necessary to investigate all potential technologies for efficiency improvement. In a combustion engine, about 2/3 of the chemical energy of the fuel is dissipated as waste heat. Due to its high temperature level, the waste heat in the exhaust gas is very promising for the technology of thermoelectric generators (TEG). In this work the methodology for a holistic TEG optimization for automotive vehicle applications will be presented. Thereby, all system interactions between the vehicle and the TEG are modelled and the CO 2 reduction can be optimized within the vehicle system. Moreover the costs are calculated for each TEG design, and the method realizes an optimization of the cost-benefit ratio in a direct way. The optimization method is applied with a highly integrated TEG design, which has been developed to be compact and lightweight. Through the combination of improvements in TEG design and system optimization, a gravimetric power density of 267 W/kg and a volumetric power density of 478 W/dm^3 could be achieved. These power densities are about 900% and 700%, respectively, higher than the state of the art. The optimization method was applied exemplarily to a conventional vehicle (Volkswagen Golf VII) and a hybrid vehicle (Opel Ampera/Chevrolet Volt). As a result, reductions in consumption and CO 2 emissions of up to 2.2% for the conventional and 3.4% for the hybrid vehicle could be achieved within the worldwide harmonized light duty driving test cycle. The cost-benefit optimum is 81.3 €/ (g/km) for the conventional vehicle and 54.8 €/(g/km) for the hybrid vehicle in charge sustaining mode.

A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space-time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to N = 1 supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity.

General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the noncommutativity algebra of the coordinates in the canonical case of noncommutative geometry, this idea is closely related to noncommutative geometry as well as to canonical quantization of gravity. According to this presupposition generalized field equations for general relativity are derived which are obtained by replacing the usual tetrad field by the tetrad field operator within the actions and then building expectation values of the corresponding field equations between coherent states. These coherent states refer to creation and annihilation operators created from the components of the tetrad field operator. In this sense the obtained theory could be regarded as a kind of semiclassical approximation of a complete quantum description of gravity. The consideration presupposes a special choice of the tensor determining the algebra providing a division of space-time into two two-dimensional planes.