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Marek Czachor

Publications and source records attributed to Marek Czachor.

101 records · Page 6Linked to original sources
arXiv1997

Bell inequality and complementarity loophole

A simple classical, deterministic, local situation violating the Bell inequality is described. The detectors used in the experiment are ideal and the observers who decide which pair of measuring devices to choose for a given pair of particles have free will. The construction uses random variables which are not jointly measurable in a single run of an experiment and the hidden variables have a nonsymmetric probability density. Such random variables are complementary but still fully classical. An assumption that classical random variables cannot satisfy any form of complementarity principle is false, and this is the loophole used in this example. A relationship to the detector inefficiency loophole is discussed.

quant-ph↗
arXiv1997

Manifestly covariant formulation of discrete-spin and real-mass unitary representations of the Poincare group

Manifestly covariant formulation of discrete-spin, real-mass unitary representations of the Poincaré group is given. We begin with a field of spin-frames associated with 4-mometa p and use them to simplify the eigenvalue problem for the Pauli-Lubanski vector projection in a direction given by a world-vector t. As opposed to the standard treatments where t is a constant time direction, our t is in general p-dependent and timelike, spacelike or null. The corresponding eigenstates play a role of a basis used to define Bargmann-Wigner spinors which form a carrier space of the unitary representation. The construction does not use the Wigner-Mackey induction procedure, is manifestly covariant and works simultaneously in both massive and massless cases (in on- and off-shell versions). Of particular interest are special Bargmann-Wigner spinors ($ω$-spinors) associated with flag pole directions of the spin-frame field $ω_A(p)$.

hep-th↗
arXiv1996

Einstein-Podolsky-Rosen-Bohm experiment with massive particles as a test of relativistic center-of-mass position operator

The nonrelativistic singlet state average $\langle ψ|{\vec a}\cdot\vec σ\otimes {\vec b}\cdot\vec σ|ψ\rangle =-\vec a\cdot\vec b $ can be relativistically generalized if one defines spin {\it via\/} the relativistic center-of-mass operator. The relativistic correction is quadratic in $v/c$ and can be measured in Einstein-Podolsky-Rosen-Bohm-type experiments with massive spin-1/2 particles. A deviation from the nonrelativistic formula would indicate that for relativistic nonzero-spin particles centers of mass and charge do not coincide.

quant-ph↗
arXiv1996

Manifestly Covariant Approach to Bargmann-Wigner Fields (I): Generalized scalar products and Wigner states

Manifestly covariant formalism for Bargmann-Wigner fields is developed. It is shown that there exists some freedom in the choice of the form of the Bargmann-Wigner scalar product: The general product depends implicitly on a family of world-vectors. The standard choice of the product corresponds to timelike and equal vectors which define a ``time" direction. The generalized form shows that formulas are simpler if one chooses {\it null\/} directions. This freedom is used to derive simple covariant formulas for momentum-space wave functions (generalized Wigner states) corresponding to arbitrary mass and spin and using eigenstates of the Pauli-Lubanski vector. The eigenstates which make formulas the simplest correspond to projections of the Pauli-Lubanski vector on {\it null\/} directions. The new formulation is an alternative to the standard helicity formalism.

quant-ph↗
arXiv1996

Manifestly Covariant Approach to Bargmann-Wigner Fields (II): From spin-frames to Bargmann-Wigner spinors

The Bargmann-Wigner (BW) scalar product is a particular case of a larger class of scalar products parametrized by a family of world-vectors. The choice of null and $p$-dependent world-vectors leads to BW amplitudes which behave as local $SU(2)$ spinors (BW-spinors) if {\it passive\/} transformations are concerned. The choice of null directions leads to a simplified formalism which allows for an application of ordinary, manifestly covariant spinor techniques in the context of infinite dimensional unitary representations of the Poincaré group.

quant-ph↗
arXiv1996

Nambu-Type Generalization of the Dirac Equation

Nonlinear generalization of the Dirac equation extending the standard paradigm of nonlinear Hamiltonians is discussed. ``Faster-than-light telegraphs" are absent for all theories formulated within the new framework. A new metric for infinite dimensional Lie algebras associated with Lie-Poisson dynamics is introduced.

quant-ph↗
arXiv1995

Simple Proof of Invariance of the Bargmann-Wigner Scalar Products

An explicitly covariant formalism for dealing with Bargmann-Wigner fields is developed. An invariance of the Barmann-Wigner norm can be proved in a unified way for both massive and massless fields. It is shown that there exists some freedom in the choice of the form of the Bargmann-Wigner scalar product.

quant-ph↗