Related papers: Generalised complex geometry in thermodynamical fl…
The quantum fluctuations of the geodesic deviation equation in a flat background spacetime are discussed. We calculate the resulting mean squared fluctuations in the relative velocity and separation of test particles. The effect of these…
A universal scheme for describing gravitational thermal effects is developed as a generalization of Unruh effect. Quasi-Rindler (QR) coordinates are constructed in an arbitrary curved space-time in such a way that the imaginary QR time be…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
Generalized complex geometry is an example of a powerful formalism to attempt the construction of a language adequate to string theory. With the remarkable property of unifying symplectic and complex manifolds as special cases of a broader…
We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to…
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…
Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of…
A generalized entropy arising in the context of superstatistics is obtained for an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric…
A new general expression is derived for the fluctuating electromagnetic field outside a metal surface, in terms of its surface impedance. It provides a generalization to real metals of Lifshitz theory of molecular interactions between…
We consider thermal effects in the propagation of gravitational waves on a cosmological background. In particular, we consider scalar field cosmologies and study gravitational modes near cosmological singularities. We point out that the…
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
When joined the unified gauge picture of fundamental interactions, the gravitation theory leads to geometry of a space-time which is far from simplicity of pseudo-Riemannian geometry of Einstein's General Relativity. This is geometry of the…
In this article we introduce a generalization of the Newton transformation to the case of a system of endomorphisms. We show that it can be used in the context of extrinsic geometry of foliations and distributions yielding new integral…
We analyze ensemble in which energy (E), temperature (T) and multiplicity (N) can all fluctuate and with the help of nonextensive statistics we propose a relation connecting all fluctuating variables. It generalizes Lindhard's thermodynamic…
Effective field theory methods suggest that some rather-general extensions of General Relativity include, or are mimicked by, certain higher-order curvature corrections, with coupling constants expected to be small but otherwise arbitrary.…
The new uncertainty relation is derived in the context of the canonical quantum theory with gravity for the case of the maximally symmetric space. This relation establishes a connection between fluctuations of the quantities which determine…
Recently, we presented a unified way of analysing classical cosmological perturbation in generalized gravity theories. In this paper, we derive the perturbation spectrums generated from quantum fluctuations again in unified forms. We…
The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some…
Under the fluctuation of the electric charge and atomic mass, this paper considers the theory of the thin film depletion layer formation of an ensemble of finitely excited, non-empty $d/f$-orbital heavy materials, from the thermodynamic…
Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…