Related papers: Notes on symmetric spaces
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
These lecture notes contain an introduction to some of the fundamental ideas and results in analysis and probability on infinite-dimensional spaces, mainly Gaussian measures on Banach spaces. They originated as the notes for a topics course…
These lecture notes provide an overview of different aspects of de Sitter space and their plausible holographic interpretations. We start with a general description of the classical spacetime. We note the existence of a cosmological horizon…
This lecture note surveys the gamma matrices in general dimensions with arbitrary signatures, the study of which is essential to understand the supersymmetry in the corresponding spacetime. The contents supplement the lecture presented by…
We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane…
Notes from 11 October 2004 lecture presented at the Joint Institute for Nuclear Astrophysics R-Matrix School at Notre Dame University.
These are lecture notes on the rigidity of submanifolds of projective space "resembling" compact Hermitian symmetric spaces in their homogeneous embeddings. Recent results are surveyed, along with their classical predecessors. The notes…
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
We propose a construction of separated quotient space and apply this construction for simple description of Study-Semple-Satake-Furstenberg-De Concini-Procesi-Oshima boundary of symmetric space
Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. The lectures covered quantum mechanics for closed systems like the universe, generalized quantum mechanics, time in…
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at…
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…
Two examples, not connected at present, from author's papers (Nuovo Cim., 1992, v.105A, p.77 [hep-th/0207210] and GRG, 1999, v.31, p.1431 [gr-qc/0207017]) are considered here in which a physical model has discrete symmetries and additional…
This is just a note for \cite[Chapter$3{1/2}_+$]{gromov}. Maybe this note is obvious for a reader who knows metric geometry. I wish that someone study further in this direction.
This is the lecture note of my invited lecture given at the International Conference on Number Theory at Harish-Chandra Research Institute in Allahabad (quite near the River Ganges), India on December 5, 2006. I gave an invited lecture on…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.
A brief summary is given of studies on supersymmetry and the spectrum of superparticles presented at the Linear Collider Workshop 2000.
These are lecture notes for the course "Poisson geometry and deformation quantization" given by the author during the fall semester 2020 at the University of Zurich. The first chapter is an introduction to differential geometry, where we…
These lecture notes are based on a course given at Institut de Physique Th\'eorique of CEA/Saclay in January/February 2013.