Modified Gravity and Cosmology

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

http://cds.cern.ch/record/503806/files/0106045.pdf

New developments in the Casimir effect

Heat kernel expansion: user's manual

Mathematical Handbook for Scientists and Engineers

The widely used nonperturbative wave functions and distribution functions of QCD are determined as matrix elements of light-ray operators. These operators appear as large momentum limit of nonlocal hadron operators or as summed up local operators in light-cone expansions. Nonforward one-particle matrix elements of such operators lead to new distribution amplitudes describing both hadrons simultaneously. These distribution functions depend besides other variables on two scaling variables. They are applied for the description of exclusive virtual Compton scattering in the Bjorken region near forward direction and the two meson production process. The evolution equations for these distribution amplitudes are derived on the basis of the renormalization group equation of the considered operators. This includes that also the evolution kernels follow from the anomalous dimensions of these operators. Relations between different evolution kernels (especially the Altarelli-Parisi and the Brodsky-Lepage) kernels are derived and explicitly checked for the existing two-loop calculations of QCD. Technical basis of these results are support and analytically properties of the anomalous dimensions of light-ray operators obtained with the help of the $\alpha$-representation of Green's functions.

http://cds.cern.ch/record/374985/files/9812448.pdf

Wave functions, evolution equations and evolution kernels from light ray operators of QCD

We present a direct approach for the calculation of functional determinants of the Laplace operator on balls. Dirichlet and Robin boundary conditions are considered. Using this approach, formulas for any value of the dimension,D, of the ball, can be obtained quite easily. Explicit results are presented here for dimensionsD=2,3,4,5 and 6.

https://projecteuclid.org/download/pdf_1/euclid.cmp/1104286875

Zeta function determinant of the Laplace operator on the D-dimensional ball

We find the combined effect of nonzero temperature and finite conductivity onto the Casimir force between real metals. Configurations of two parallel plates and a sphere (lens) above a plate are considered. Perturbation theory in two parameters (the relative temperature and the relative penetration depth of zero-point oscillations into the metal) is developed. Perturbative results are compared with computations. Recent improper computations based on the Lifshitz formula for the temperature Casimir force are discussed.

https://arxiv.org/pdf/quant-ph/0003021.pdf

Casimir force at both nonzero temperature and finite conductivity.

The Altarelli-Parisi Kernel as Asymptotic Limit of an Extended Brodsky-Lepage Kernel

The Casimir and van der Waals interaction between two dissimilar thick dielectric plates is reconsidered on the basis of thermal quantum field theory in Matsubara formulation. We briefly review two main derivations of the Lifshitz formula in the framework of thermal quantum field theory without use of the fluctuation-dissipation theorem. A set of special conditions is formulated under which these derivations remain valid in the presence of dissipation. The low-temperature behavior of the Casimir and van der Waals interactions between dissimilar dielectrics is found analytically from the Lifshitz theory for both an idealized model of dilute dielectrics and for real dielectrics with finite static dielectric permittivities. The free energy, pressure, and entropy of the Casimir and van der Waals interactions at low temperatures demonstrate the same universal dependence on the temperature as was previously discovered for ideal metals. The entropy vanishes when temperature goes to zero proving the validity of the Nernst heat theorem. This solves the long-standing problem on the consistency of the Lifshitz theory with thermodynamics in the case of dielectric plates. The obtained asymptotic expressions are compared with numerical computations for both dissimilar and similar real dielectrics and found to be in excellent agreement. The role of the zero-frequency term in Matsubara sum is investigated in the case of dielectric plates. It is shown that the inclusion of conductivity in the model of dielectric response leads to the violation of the Nernst heat theorem. The applications of this result to the topical problems of noncontact atomic friction and the Casimir interaction between real metals are discussed.

https://arxiv.org/pdf/quant-ph/0510054.pdf

Bodo Geyer

Papers

Wave functions, evolution equations and evolution kernels from light ray operators of QCD

Zeta function determinant of the Laplace operator on the D-dimensional ball

Casimir force at both nonzero temperature and finite conductivity.

The Altarelli-Parisi Kernel as Asymptotic Limit of an Extended Brodsky-Lepage Kernel

Thermal quantum field theory and the Casimir interaction between dielectrics