Related papers: The Superspace of Geometrodynamics
It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is…
We investigate cosmological models in a recently proposed geometrical theory of gravity, in which the scalar field appears as part of the space-time geometry. We extend the previous theory to include a scalar potential in the action. We…
I review the conceptual, algebraical, and geometrical structure of Doubly Special Relativity. I also speculate about the possible relevance of DSR for quantum gravity phenomenology.
In quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle H…
This is an expository paper about the geometry of the torsion constraints in the superspace formulation of supergravity theories. It was prepared for the 2001 Park City Research Program in Supergeometry.
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
In the absence of a complete theory of quantum gravity, phenomenological models built upon minimal assumptions have been explored for the analysis of possible quantum effects in gravitational systems. Implications of a superposition of…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum…
Two-dimensional pure electrodynamics is mapped into two-dimensional gravity in the first order formalism at classical and quantum levels. Due to the fact that the degrees of freedom of these two theories do not match, we are enforced to…
This article reviews the subject of supersymmetry and its breaking. The emphasis is on recent developments in metastable, dynamical supersymmetry breaking, which permit the construction of promising models of particle physics.
We give a new interpretation for the super loop space that has been used to formulate supersymmetry. The fermionic coordinates in the super loop space are identified as the odd generators of the Weil algebra. Their bosonic superpartners are…
The basic mathematical framework for super Hilbert spaces over a Grassmann algebra with a Grassmann number-valued inner product is formulated. Super Hilbert spaces over infinitely generated Grassmann algebras arise in the functional…
A new concept of the constitution of Nature is proposed. The constructed submicroscopic quantum mechanics is deterministic and is characterised by elementary excitations of the space net that is treated as the tessellation of balls, or…
We study aspects of 3d $\mathcal{N}=2$ supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the…
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…
A cosmological model with perfect fluid and self-interacting quintessence field is considered in the framework of the spatially flat Friedmann-Robertson-Walker (FRW) geometry. By assuming that all physical quantities depend on the volume…
We analyze a static and spherically symmetric hairy black hole solution in non-invariant massive gravity. The formalism of geometrothermodynamics is used to describe the thermodynamic characteristics of this black hole in a Legendre…
The classical field equations of general relativity can be expressed as a single geodesic equation, describing the free fall of a point particle in superspace. Based on this formulation, a ``worldline'' quantization of gravity, analogous to…
We review and discuss some recent developments on the unconventional interaction between superconducting systems and the local gravitational field. While it is known that gravitational perturbations (such as gravitational waves) can affect…