Related papers: An Algebraic Approach to Physical Fields
In the last decades the logico-algebraic approach to quantum mechanics turned to be a successful tool to render the quantum mechanical formalism on a steady operationalistic background. The algebraic approach to general relativity first…
The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise…
We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
We describe the geomety of a set of scalar fields coupled to gravity. We consider the formalism of a differential Z_2-graded algebra of $2\times 2$ matrices whose elements are differential forms on space-time. The connection and the…
Spinors are central to physics: all matter (fermions) is made of spinors, and all forces arise from symmetries of spinors. It is common to consider the geometric (Clifford) algebra as the fundamental edifice from which spinors emerge. This…
As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states, and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism…
We present a new metaphysical framework for physics that is conceptually clear, ontologically parsimonious, and empirically adequate. This framework relies on the notion of self-subsisting structure, that is, a set of fundamental physical…
The well-known geometric approach to field theory is based on description of classical fields as sections of fibred manifolds, e.g. bundles with a structure group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms…
In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
Based on a family of indefinite unitary representations of the diffeomorphism group of an oriented smooth $4$-manifold, a manifestly covariant $4$ dimensional and non-perturbative algebraic quantum field theory formulation of gravity is…
Using the language of the Geometric Algebra, we recast the massless Dirac bispinor as a set of Lorentz scalar, bivector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism. The spinor's unusual…
The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…
In the field theories with twistor structure particles can be identified with (spacially bounded) caustics of null geodesic congruences defined by the twistor field. As a realization, we consider the ``algebrodynamical'' approach based on…
In this paper we will analyse a scalar field theory on a spacetime with noncommutative and non-anticommutative coordinates. This will be done using supermanifold formalism. We will also analyse its quantization in path integral formalism.
In this memoir, we seek to construct a dynamical theory as complete as possible to describe the algebraic properties of the field of real numbers in constructive mathematics without axiom of dependent choice. We propose a theory which turns…
We investigate dynamics of scalar field with non-minimal kinetic term. Nontrivial behavior of the field in the vicinity of singular points of kinetic term is observed. In particular, the singular points could serve as attractor for…
Configuration spaces of many real mechanical systems appear to be manifolds with singularity. A singularity often indicates that geometry of motion may change at the singular point of configuration space. We face conceptual problem…
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…