Markus Lederer ([email protected]) is Assistant Professor for International Relations at the University of Potsdam, Germany, and is assistant project manager of the research project D3 “New Modes of Governance in Climate Protection: Green companies in Newly Industrializing Countries” of the Collaborative Research Centre SFB 700 ’Governance in Areas of Limited Statehood’ (www.sfb-governance...

Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed bose and fermi representations. The construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized Gree...

In this paper we derive several improved forms of the Jensen inequality, giving the necessary and sufficient conditions for them to hold in the case of the real Stieltjes measure not necessarily positive. The obtained relations are characterized via the Green function. As an application, our main results are employed for constructing some classes of exponentially convex functions and some Cauch...

A convenient formalism is developed to treat classical dynamical systems involving (p = 2) parafermionic and parabosonic dynamical variables. This is achieved via the introduction of a parabracket which summarizes the paracommutation relations of the corresponding Green components in a uni ed manner. Furthermore, it is shown that Peierls quantization scheme may be applied to such systems provid...

A graded K-algebra R has property Np if it is generated in degree 1, has relations in degree 2 and the syzygies of order ≤ p on the relations are linear. The GreenLazarsfeld index of R is the largest p such that it satisfies the property Np. Our main results assert that (under a mild assumption on the base field) the c-th Veronese subring of a polynomial ring has Green-Lazarsfeld index ≥ c+1. T...

Some time ago Takahashi derived so called transverse relations relating Green’s functions of different orders to complement the well-knownWard-Green-Takahashi identities of gauge theories by considering wedge rather than inner products. These transverse relations have the potential to determine the full fermion-boson vertex in terms of the renormalization functions of the fermion propagator. Fo...

The concept of second entropy is introduced for the dynamic transitions between macrostates. It is used to develop a theory for fluctuations in velocity, and is exemplified by deriving Onsager reciprocal relations for Brownian motion. The cases of free, driven, and pinned Brownian particles are treated in turn, and Stokes' law is derived. The second entropy analysis is applied to the general ca...

In the propagation of an electron through a 1D asymmetric complex potential, it is known that while the conventional Green function reciprocity symmetry will ensure transmission to be symmetric between a “left-incident” and a “right-incident” beam, no such symmetry exists for the case of reflection. Here we derive generalized reciprocity relations for both the amplitude and phase of the reflect...

We demonstrate that parastatistics can be quantized using path integrals by calculating the generating functionals for time-ordered products of both free and interacting parabose and parafermi fields in terms of path integrals. We also give a convenient form of the commutation relations for the Green components of the parabose and parafermi operators in both the canonical and path integral form...

A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski equality is recovered in the case this observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity relations are deduced thereof in the l...