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Jerzy Hanckowiak

Publications and source records attributed to Jerzy Hanckowiak.

12 recordsLinked to original sources
arXiv2015

Equations for generalized n-point information with extreme and not extreme approximations in the free Fock space

The general n-point information (n-pi) are introduced and equations for them are considered. The role of right and left invertible interaction operators occurring in these equations together with their interpretation is discussed. Some comments on approximations to the proposed equations are given. The importance of positivity conditions and a possible interpretation of n-pi in the case of their non-compliance, for essentially non-linear interactions (ENI), are proposed. A language of creation, annihilation and projection operators which can be applied in classical as well as in quantum case is used. The role of the complex numbers and functions in physics is also a little elucidated.

physics.gen-ph↗
arXiv2014

An algebraic approach to systems with dynamical constraints

Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's theorem is obtained and constraints are also considered in the phase space.

physics.gen-ph↗
arXiv2013

Algebraic analysis of linear systems with double type of perturbations

Linear systems under the influence of nonlinear and random linear perturbations, and with random initial and boundary conditions, are discussed. The notion of states of a system is substituted by the notion of the generating vectors for n-point information (n-pi), n=0,1,2,..., characterizing a system at different space-time points. A complete system of equations for physical n-pi are derived and certain universal expansions are proposed.

physics.gen-ph↗
arXiv2012

Metaphysics of the free Fock space with local and global information

A new interpretation of the basic vector |0> of the free Fock space (FFS) and the FFS is proposed. The approximations to various equations with additional parameters, for n-point information (n-pi), are also considered in the case of non-polynomial nonlinearities.

physics.gen-ph↗
arXiv2011

Local and global information and equations with left and right invertible operators in the free Fock space

The subject of the work is short description of huge amount of n-point information (n-pi) about the system. Methods for solving equations that satisfy such information are considered. Possible interpretation of left and right invertible operators appearing in these equations is also proposed. For local information, the creation and annihilation operators satisfying the Cuntz relations are introduced. It is also introduced the vector describing the local vacuum which completes the equation for n-pi with a global information. An important components of the work are examples of local operator-valued functions.

physics.gen-ph↗
arXiv2011

Unification of some classical and quantum ideas

The free Fock space with corresponding - information creation and anihilation operators - supplies a kind of extended language in which equations for n-point information (n-pi) of classical and quantum physics are described. In this description the space and time are treated in a similar manner and even different reference systems are treated in a more democratic way. The information vacuum vectors in both the classical and quantum case are introduced. Restrictions upon n-pi leading to complete equations are derived. The paper also draws attention to the fact that averaging or smoothing of the original quantities (filtration) is not only consistent with the experimental capabilities of people, but it is also an important tool to understand the reality.

physics.gen-ph↗
arXiv2010

Free Fock space and functional calculus approach to the n-point information about the "Universe"

Starting from a differential equation for the unique field, the equation for the generating vector |V> of the n-point information (correlation and smeared functions) in the free Fock space is derived. In derived equation, due to appropriate extension of the right invertible operators, the physical vacuum vector |0> appears with a global characteristic of the field. For so called resolvent regularization of the original systems, the closed equations for the n-point information are analysed with the help of functional calculus.

physics.gen-ph↗
arXiv2010

Models of the "Universe" and a Closure Principle

Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and experimental ability is considered and reduced to appropriate additional conditions imposed on solutions.

physics.gen-ph↗
arXiv2008

Some Insight into Many Constituent Dynamics

A description of many constituent (particle) systems with fuzzy initial conditions is proposed with the help of the field language. In this language correlation functions are defined and equations for them are derived in the free Fock space. Additional conditions for their solutions are postulated. The closure problem for polynomial, rational, local and nonlocal interactions is considered with exploitation of left or right invertibility of used operators. Some general remarks concerning symmetry and multi-scale descriptions are given.

math-ph↗
arXiv2005

Reynolds' Dream?

Equations for correlation functions, here referred to as Reynolds- Kraichnan-Lewis equations (RKLE), are considered and their wide application is indicated. Perturbation and non-perturbation solutions are given. To elucidate a closure problem - various forms of equations are presented. Exact, closed equations for the projected correlation functions are derived.

physics.flu-dyn↗
arXiv2004

Rectangular Parallelepiped Vibration in Plane Strain State

In this paper we present a vibration spectrum of a homogenous parallelepiped (HP) under the action of volume and surface forces resulting from the exponent displacements entering the Fourier transforms. Vibration under the action of axial surface tractions and the free vibration are described separately. A relationship between the high frequency vibration and boundary conditions (BC) is also considered.

physics.class-ph↗