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Bozhidar Z. Iliev

Publications and source records attributed to Bozhidar Z. Iliev.

At least 19 recordsLinked to original sources
arXiv2014

Measuring the evaluation and impact of scientific works and their authors

Problems for evaluation and impact of published scientific works and their authors are discussed. The role of citations in this process is pointed out. Different bibliometric indicators are reviewed in this connection and ways for generation of new bibliometric indices are given. The influence of different circumstances, like self-citations, number of authors, time dependence and publication types, on the evaluation and impact of scientific papers are considered. The repercussion of works citations and their content is investigated in this respect. Attention is paid also on implicit citations which are not covered by the modern bibliometrics but often are reflected in the peer reviews. Some aspects of the Web analogues of citations and new possibilities of the Internet resources in evaluating authors achievements are presented.

physics.soc-ph↗
arXiv2012

Transformation laws of the components of classical and quantum fields and Heisenberg relations

The paper recalls and point to the origin of the transformation laws of the components of classical and quantum fields. They are considered from the "standard" and fibre bundle point of view. The results are applied to the derivation of the Heisenberg relations in quite general setting, in particular, in the fibre bundle approach. All conclusions are illustrated in a case of transformations induced by the Poincaré group.

math-ph↗
arXiv2010

A mathematical base for Fibre bundle formulation of Lagrangian Quantum Field Theory

The paper contains a differential-geometric foundations for an attempt to formulate Lagrangian (canonical) quantum field theory on fibre bundles. In it the standard Hilbert space of quantum field theory is replace with a Hilbert bundle; the former playing a role of a (typical) fibre of the letter one. Suitable sections of that bundle replace the ordinary state vectors and the operators on the system's Hilbert space are transformed into morphisms of the same bundle. In particular, the field operators are mapped into corresponding field morphisms.

math-ph↗
arXiv2008

Heisenberg relations in the general case

The Heisenberg relations are derived in a quite general setting when the field transformations are induced by three representations of a given group. They are considered also in the fibre bundle approach. The results are illustrated in a case of transformations induced by the Poincare group.

math-ph↗
arXiv2008

Links between connections, parallel transports, and transports along paths in differentiable fibre bundles

The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts "connection" and "(axiomatically defined) parallel transport" is established. Some results which are specific for topological and vector bundles are presented.

math.DG↗
arXiv2007

On the axiomatization of "parallel transports" and and one its generalization

A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along paths are pointed as a generalization of the (axiomatically defined) parallel transports. Some properties of the general transports along paths are presented.

math-ph↗
arXiv2007

Lagrangian quantum field theory in momentum picture. IV. Commutation relations for free fields

Possible (algebraic) commutation relations in the Lagrangian quantum theory of free (scalar, spinor and vector) fields are considered from mathematical view-point. As sources of these relations are employed the Heisenberg equations/relations for the dynamical variables and a specific condition for uniqueness of the operators of the dynamical variables (with respect to some class of Lagrangians). The paracommutation relations or some their generalizations are pointed as the most general ones that entail the validity of all Heisenberg equations. The simultaneous fulfillment of the Heisenberg equations and the uniqueness requirement turn to be impossible. This problem is solved via a redefinition of the dynamical variables, similar to the normal ordering procedure and containing it as a special case. That implies corresponding changes in the admissible commutation relations. The introduction of the concept of the vacuum makes narrow the class of the possible commutation relations; in particular, the mentioned redefinition of the dynamical variables is reduced to normal ordering. As a last restriction on that class is imposed the requirement for existing of an effective procedure for calculating vacuum mean values. The standard bilinear commutation relations are pointed as the only known ones that satisfy all of the mentioned conditions and do not contradict to the existing data.

hep-th↗
arXiv2006

Handbook of normal frames and coordinates

The main subject of the book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in differential geometry. The book can be used as a reference manual, review of the existing results and introduction to some new ideas and developments. In the book can be found practically all existing essential results and methods concerning normal frames and coordinates. Most of the results are represented in full detail with full, in some cases new, proofs. All classical results are expanded and generalized in various directions. Theorems of existence, uniqueness and, possibly, holonomicity of the normal frames and coordinates are proved; mostly, the proofs are constructive and some their parts can be used independently for other tasks. Besides published results, their extensions and generalizations, the book contains completely new results which appear for the first time.

math.DG↗
arXiv2006

Linear vector fields and exponential law

The paper is devoted to vector fields on the spaces R^2 and R^3, their flow and invariants. Attention is plaid on the tensor representations of the group GL(2,R) and on fundamental vector fields. The rotation group on R^3 is generalized to rotation groups with arbitrary quadrics as orbits.

math.DG↗
arXiv2006

Affine and fundamental vector fields

This is a review with examples concerning the concepts of affine (in particular, constant and linear) vector fields and fundamental vector fields on a manifold. The affine, linear and constant vector fields on a manifold are shown to be in a bijective correspondence with the fundamental vector fields on it of respectively general affine, general linear and translation groups (locally) represented on the manifold via the described in this work left actions; in a case of the manifolds R^n and C^n, the actions mentioned have the usual meaning of affine, linear and translation transformations.

math.DG↗
arXiv2005

Deviation equations in spaces with affine connection

Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained on this base. This is done via imposing certain conditions on the Lie derivatives with respect to the tangential vector of the basic trajectory.

math.DG↗
arXiv2005

Lagrangian quantum field theory in momentum picture. III. Free vector fields

Free vector fields, satisfying the Lorenz condition, are investigated 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 commutation relations are derived. Some problems concerning the vacuum and state vectors of free vector field are discussed. Special attention is paid to peculiarities of the massless case; in particular, the electromagnetic field is explored. Several Lagrangians, describing free vector fields, are considered and the basic consequences of them are pointed and compared.

hep-th↗
arXiv2005

Linear transports along paths in vector bundles. IV. Consistency with bundle metrics

The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All metrics (resp. transports) consistent with a given transport (resp. metric) are explicitly obtained. The special case of linear transports, generated by derivations of tensor algebras, of vectors is considered. Analogous problems are investigated in complex vector bundles endowed with Hermitian metrics.

math.DG↗