A relativistically invariant mass operator

In Ukrain. J. Phys., 1967, V.12, N 5, p.741-746 it was shown how, for a given (discrete) mass spectrum of elementary or hypothetical particles, it was possible to construct a non-trivial algebra G containing a Poincare algebra P as a subalgebra so that the mass operator, defined throughout the space where one of the irreducible representations G is given, is self-conjugate and its spectrum coincides with the given mass spectrum. Such an algebra was constructed in explicit form for the nonrelativistic case, i.e., the generators were written for the algebra. However, the problem of how to assign the algebra G constructively and determine an explicit form of the mass operator in the relativistic case has remained unsolved. In the present work we present a solution of this problem, construct continuum analogs of the classical algebras U(N) and Sp(2N), and show that the problem of including the Poincare algebra can be formulated in the language of wave function equations.Comment: 11 page

On the three types of relativistic equations for particles with nonzero mass

In previous papers quant-ph/0206077, quant-ph/0206078, quant-ph/0206079 we have shown that there exist three types of the relativistic equations for the massless particles. Here we show that for the free particles and antiparticles with the mass m>0 and the arbitrary spin $s \geq 1/2$ there also exist three types of nonequivalent equations.Comment: 3 page

P, T, C properties of the Poincare invariant equations for massive particles

We have shown quant-ph/0206104 (Lett. Nuovo Cimento, 1972, 4, 344) that for free particles and antiparticles with mass m>0 and arbitrary spin s>0, in the framework of the Poincare group P(1,3), there exist three types of nonequivalent equations. In the present paper we study the P, T, C properties of these equations.Comment: 5 page

Equations of motion in odd-dimensional spaces and T-, C-invariance

The properties of the equation of Dirac type in three-dimensional and five-dimensional Minkowski space-time with respect to time reflection (in sense of Pauli and Wigner) as well as to the operation of charge conjugation are investigated. P-, T-, C-invariance of Dirac equation for the cases of four components (in three-dimentional space) and eight components (in five-dimensional space) is established. Within the framework of the Poincare group a relativistic equation is suggested wich describes the movement of a particle with non-fixed (indefinite) mass in external electromagnetic field.Comment: 7 page

On the P- and T-non-invariant two-component equation for the neutrino

The relativistic two-component equation describing the free motion of particles with zero mass and spin 1/2, which is P- and T-non-invariant but C-invariant, is found. The representation of the Poincare group for zero mass and discrete spin is constructed. The position operator for such a particle is defined.Comment: 8 page

On a motion equation for two particles in relativistic quantum mechanics

The purpose of the present note is to propose, in the framework of relativistic quantum mechanics, a new Poincare-invariant equation for two particles with masses m_1, m_2 and spin s_1=s_2=1/2. It is a first-order linear differential equation for the eight-component wave function. With the help of this equation the description of the motion of two-particle systems is reduced to the description of one-particle systems in the (1+6)-dimensional Minkowski space which can be in two spin states (s=0 or s=1).Comment: 4 page

Qubit decoherence due to detector switching

We provide insight into the qubit measurement process involving a switching type of detector. We study the switching-induced decoherence during escape events. We present a simple method to obtain analytical results for the qubit dephasing and bit-flip errors, which can be easily adapted to various systems. Within this frame we investigate potential of switching detectors for a fast but only weakly invasive type of detection. We show that the mechanism that leads to strong dephasing, and thus fast measurement, inverts potential bit flip errors due to an intrinsic approximate time reversal symmetry.Comment: 5 pages, 5 figure

Dynamical tunneling in macroscopic systems

We investigate macroscopic dynamical quantum tunneling (MDQT) in the driven Duffing oscillator, charateristic for Josephson junction physics and nanomechanics. Under resonant conditions between stable coexisting states of such systems we calculate the tunneling rate. In macroscopic systems coupled to a heat bath, MDQT can be masked by driving-induced activation. We compare both processes, identify conditions under which tunneling can be detected with present day experimental means and suggest a protocol for its observation.Comment: 4 pages, 3 figure

On the possible types of equations for zero-mass particles

There are a number of papers dedicated to the description of free particles and antiparticles with zero mass and spin 1/2. A great many equations with different C, P, T properties have been proposed and the impression could be formed that there are many nonequivalent theories for zero-mass particles. The purpose or this paper is to show that it is not the case and to describe all nonequivalent equations.Comment: 4 page

On the CP-noninvariant equations for the particle with zero mass and spin s=1/2

One of us quant-ph/0206077 (Nucl. Phys. B, 1970, 21, 321) has shown that for the particle with zero mass and spin s=1/2 there are three types of two-component equations (or one four-component equation with three different subsidiary conditions) which differ from one another by P, T and C properties. One of these equations is the two-component Weyl equation. In this note we give two other relativistic invariant equations.Comment: 2 page