Related papers: Geometric formulation of the Covariant Phase Space…

Motivated by the study of physical models associated with General Relativity, we review some finite-dimensional, geometric and covariant formulations that allow us to characterize in a simple manner the symmetries for classical field theory…

This paper develops 'covariant tomography', a local framework for solving Inverse Boundary Value Problems (IBVP) for parallel transport equation on star-shaped domains. By integrating geometric decomposition with specific interior…

The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and…

We present an Eilenberg-Steenrod-like axiomatic framework for equivariant coarse homology and cohomology theories. We also discuss a general construction of such coarse theories from topological ones and the associated transgression maps. A…

A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $\gamma -$law…

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group.…

Geometrically the phase space of a mechanical system involves the co-tangent bundle of the configuration space. The phase space of a relativistic field theory is infinite dimensional and can be endowed with a symplectic structure defined in…

We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial…

We analyze topological phase transitions and higher Berry curvature in one-dimensional quantum spin systems, using a framework that explicitly incorporates the symmetry group action on the parameter space. Based on a $G$-compatible…

We consider the linear space of composite fields as an infinite dimensional vector bundle over the theory space whose coordinates are simply the parameters of a renormalized field theory. We discuss a geometrical expression for the short…

The new relativistic equations of motion for the particles with spin s=1, s=3/2, s=2 and nonzero mass have been introduced. The description of the relativistic canonical quantum mechanics of the arbitrary mass and spin has been given. The…

We define a complex relativistic phase space which is the space $\mathbb{C}^4$ equipped with the Minkowski metric and with a geometric tri-product on it. The geometric tri-product is similar to the triple product of the bounded symmetric…

In this contribution, a mathematical framework is constructed to relate and compare non-linear partial differential equations (PDEs) in the category of smooth manifolds. In particular, it can be used to compare those aspects of field…

There are two methods to study families of conformal theories in the operator formalism. In the first method we begin with a theory and a family of deformed theories is defined in the state space of the original theory. In the other there…

Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…

This is a survey of a new type of relativistic space-time framework; the so-called quasi-metric framework. The basic geometric structure underlying quasi-metric relativity is quasi-metric space-time; this is defined as a 4-dimensional…

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…

Topological phases of matter in (2+1) dimensions are commonly equipped with global symmetries, such as electric-magnetic duality in gauge theories and bilayer symmetry in fractional quantum Hall states. Gauging these symmetries into local…

The aim of this paper is to provide a largely self-contained, compact and comprehensible introduction to the basic ideas behind correlation geometry, which underlies the theory of causal fermion system (CFS). A key focus here is on the…

Vector spaces of (framed) BPS states of Lagrangian four-dimensional N=2 field theories can be defined in semiclassical chambers in terms of the $L^2$-cohomology of Dirac-like operators on monopole moduli spaces. This was spelled out…