Related papers: Perturbations vs deformations
In order to study gravitational waves in any realistic astrophysical scenario, one must consider geometry perturbations up to second order. Here, we present a general technique for studying linear and quadratic perturbations on a spacetime…
Quantum affine bundles are quantum principal bundles with affine quantum structure groups. A general theory of quantum affine bundles is presented. In particular, a detailed analysis of differential calculi over these bundles is performed,…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
We have one more look at the (homological) perturbation lemma and we point out some non-standard consequences, including the relevance to deformations.
This series of lectures consists of two parts. In the first part the foundations of perturbative and non perturbative formulation are discussed. The ambiguity in the definition of vacuum condensates is then analyzed. In the second part the…
This is a revised version of gr-qc/9304033
Defects are a useful tool in the study of quantum field theories. This is illustrated in the example of two-dimensional conformal field theories. We describe how defect lines and their junction points appear in the description of symmetries…
This paper describes and proves a canonical procedure to decouple perturbations and optimize their gauge around backgrounds with one non-homogeneous dimension, namely of co-homogeneity 1, while preserving locality in this dimension.…
We give an explicit relation, up to second-order terms, between scalar-field fluctuations defined on spatially-flat slices and the curvature perturbation on uniform-density slices. This expression is a necessary ingredient for calculating…
In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical…
Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are…
The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value…
The invariance of physical observables under redefinitions of the quantum fields is a well-known and important property of quantum field theory. We study perturbative field redefinitions in effective theories, paying special attention to…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
In this dissertation the notion of deformation quantization of principal fibre bundles is established and investigated in order to find a geometric formulation of classical gauge theories on noncommutative space-times. As a generalization,…
Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. After reviewing the general framework of the second-order gauge-invariant perturbation theory, we show the fact that…
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum…
Expository paper on the relations between perturbation theory of pseudo-differential operators, finiteness theorems and deformations of Lagrangian varieties.
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution…
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…