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Bozhidar Z. Iliev

Publications and source records attributed to Bozhidar Z. Iliev.

At least 37 records · Page 2Linked to original sources
arXiv2005

Normal frames and linear transports along paths in vector bundles

The theory of linear transports along paths in vector bundles, generalizing the parallel transports generated by linear connections, is developed. The normal frames for them are defined as ones in which their matrices are the identity matrix or their coefficients vanish. A number of results, including theorems of existence and uniqueness, concerning normal frames are derived. Special attention is paid to the important case when the bundle's base is a manifold. The normal frames are defined and investigated also for derivations along paths and along tangent vector fields in the last case. It is proved that normal frames always exist at a single point or along a given (smooth) path. On other subsets normal frames exist only as an exception if (and only if) certain additional conditions, derived here, are satisfied. Gravity physics and gauge theories are pointed out as possible fields for application of the results obtained.

gr-qc↗
arXiv2005

Transports along paths in Fibre Bundles. I. General Theory

Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.

math.DG↗
arXiv2004

Linear Transports along Paths in Vector Bundles. II. Some Applications

The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor algebras are investigated. A possible generalization of the theory of geodesics is proposed when the parallel transport generated by a linear connection is replaced with an arbitrary linear transport along paths in the tangent bundle.

math.DG↗
arXiv2004

Linear Transports along Paths in Vector Bundles. I. General Theory

The (parallel) linear transports along paths in vector bundles are axiomatically described. Their general form and certain properties are found. It is shown that these transports are locally (i.e. along every fixed path) always Euclidean ones in a senses that there exist frames in which their matrices are unit. The investigated transports along paths are described in terms of their local coefficients, as well as in terms of derivations along paths.

math.DG↗
arXiv2004

Normal frames for general connections on differentiable fibre bundles

The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The existence of bundle coordinates normal at a given point and/or along injective horizontal path is proved. A necessary and sufficient condition of existence of bundle coordinates normal along injective horizontal mappings is derived.

math.DG↗
arXiv2004

Lagrangian quantum field theory in momentum picture. II. Free spinor fields

Free spinor fields, with spin 1/2, are explored in details in the momentum picture of motion in Lagrangian quantum field theory. The field equations are equivalently written in terms of creation and annihilation operators and on their base the anticommutation relations are derived. Some problems concerning the vacuum and state vectors of free spinor field are discussed. Several Lagrangians, describing free spinor fields, are considered and the basic consequences of them are investigated.

hep-th↗
arXiv2004

Lagrangian quantum field theory in momentum picture. I. Free scalar fields

The work contains a detailed investigation of free neutral (Hermitian) or charged (non-Hermitian) scalar fields and the describing them (system of) Klein-Gordon equation(s) in momentum picture of motion. A form of the field equation(s) in terms of creation and annihilation operators is derived. An analysis of the (anti-)commutation relations on its base is presented. The concept of the vacuum and the evolution of state vectors are discussed.

hep-th↗
arXiv2004

Generalized Doppler effect in spaces with a transport along paths

An analog of the classical Doppler effect is investigated in spaces (manifolds) whose tangent bundle is endowed with a transport along paths, which, in particular, can be parallel one. The obtained results are valid irrespectively to the particles mass, i.e. they hold for massless particles (e.g. photons) as well as for massive ones.

math-ph↗
arXiv2003

Momentum picture of motion in Lagrangian quantum field theory

The basic aspects of the momentum picture of motion in Lagrangian quantum field theory are given. Under some assumptions, this picture is a 4-dimensional analogue of the Schrödinger picture: in it the field operators are constant, spacetime-independent, while the state vectors have a simple, exponential, spacetime-dependence. The role of these assumptions is analyzed. The Euler-Lagrange equations in momentum picture are derived and attention is paid on the conserved operators in it.

hep-th↗
arXiv2003

Relative mechanical quantities in spaces with a transport along paths

The concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If the tangent bundle is endowed also with a metric, it gives rise also to the notion of a relative energy. Certain ties between these quantities are considered. The cases of massless particles and of special relativity are presented in this context.

math-ph↗
arXiv2003

On some generalizations of the Jacobi identity. II

On the basis of the generalizations of the Jacobi identity found by the author some identities satisfied by the curvature and torsion of a covariant differentiation are derived. A kind of the generalized covariant differentiation is proposed and a method of finding some of satisfied by them identities is given in the correspondence to the curvatures concerned.

math.DG↗
arXiv2003

Special bases for derivations of tensor algebras. II. The case along paths

The existence of local bases in which the components of derivations of tensor algebras over a differentiable manifold vanish along paths is proved. The holonomicity of these bases is investigated. The obtained results are applied to the case of linear connections. Some relations with the equivalence principle are shown.

math.DG↗