Regular Series


Vol. 23 (1992), No. 7, pp. 733 – 814


Towards Gauge Principle for Semigroups

abstract

The standard gauging procedure is extended to the (super)semigroups consisting of a disjoint subgroup being the ordinary group of internal symmetry and an ideal containing noninvertible transformations arising in supersymmetric theories. The analogue of the conjugation is brought m and used when deriving the nondiagonal gauge-like transformations which are proper for the nondiagonal covariance proposed. The latter is the origin of a new unavoidable field lying in the same representation as the usual gauge field and giving rise to the effect like torsion. The operator bilinear in these fields, which generalizes the covariant derivative in the adjoined representation, is given. The possible form of the Lagrangian and equation of motion is outlined.


The Measurement of Red-Shift and Flat Time

abstract

The measurement of the red-shift (R-S) effect of the general theory of relativity (GTR) resorts to the existence of two essentially different kinds of metrical objects: a) the macro-corpuscules of rigid bodies and the clocks which constitute reference bodies \(\bar S\) and b) the light signals never at rest with regard to any reference body, which interconnect different regions of the metrical spacetime found by \(\bar S\)’s. Our aim is to show that the comparison of frequencies of the photons emitted by atomic clocks at different spacetime regions must call for flat time continuum. Thus quantum physics which integrates the wave and the corpuscular aspects of microobjects would distinguish flat spacetime. It must be remembered that owing to its nonlocality, quantum theory is capable of reproducing stable, extended objects from the hypothetical structureless constituents. Thus it provides us with a complete theory, whereas any classical theory \((\hbar = 0)\), in particular the GTR, remains incomplete.


Calculation of the Perturbation Series to 9-th Order in a High Energy Limit of the Gauge Field Theory

abstract

Perturbation expansion for the imaginary part of the elastic fermion–fermion amplitude in the vacuum channel for the high energy limit (LLA) of the gauge field theory is calculated to the 9-th order in \(\alpha \). Technical and numerical details of the calculations are discussed.


A Measurement of \(\Lambda ^+_c\) Spin Using the \(\Lambda ^+_c \to pK^-\pi ^+\) Decay Channel

abstract

We attempt to determine the spin of the charmed baryon \(\Lambda ^+_c\) investigating the angular distribution of the direction of the normal to the decay plane in the Jackson frame for the three-body weak decay \(\Lambda ^+_c \to pK^-\pi ^+\). The method is effective even for a small number of events. This is demonstrated for a sample of 121 \(\Lambda ^+_c \to pK^-\pi ^+\) decays from NA32 experiment. The results are entirely consistent with \(J =\) \({}^1\!/\!{}_2\) assignment for the \(\Lambda ^+_c\). The spin formalism for a three-body weak decay of a baryon is extensively described.


Higgs Mechanism as the Manifestation of an Intrinsic Coupling of “Visible” and “Hidden” Degrees of Freedom

abstract

First, we summarize the recently proposed idea of leptons and quarks composed of algebraic degrees of freedom (defined by Clifford algebras) that justifies the existence of three and only three replicas of the fundamental fermions (as e.g. \(e^-, \mu ^-, \tau ^-\)). Then, we find within this algebraic scheme a possible place for Higgs scalar and pseudoscalar, both appearing in two replicas.


SU(1,1)/U(1) Coset Gauge Theory

abstract

We construct and investigate an Abelian gauge theory on the SU(l,1)/U(1) coset base space. We determine the space of flat connections and solutions of Maxwell equations. The relations to the two-dimensional euclidean black hole are discussed. We study also the interactions of the scalar field with the vacuum of considered model.


Variation of the Fermi Matrix Elements of \(\Delta J=0\,\,\,\,\Delta T=1\) Beta Decays with the Size Parameter

abstract

Contributions to the Fermi matrix elements \(M_F\) of \(\Delta J=0, \Delta T=1\) beta decays arise mainly from the Coulomb and the specifically nuclear charge-dependent effects, for which the short-range phenomenological potential of Blin-Stoyle & Le Tonrneux is used. Using \(jj\)-coupling shell model with harmonic oscillator wavefunctions, it is found that in the region of interest, the fractional change in \(M_F\) is approximately equal but opposite to the fractional change in the size parameter.


The Temperature Dependence of the Level Density Parameter

abstract

Using the Thomas–Fermi model and the leptodermous expansion in powers of \(A^{1/3}\), we derive a formula for nuclear level density parameter “a” at finite temperature. The level density parameter was found to depend on the nuclear potential only through the effective mass \(m^*/m\). The experimental data of “a” at zero temperature favours a value of \(m^*/m \approx 1\). The level density parameter was found to decrease with increasing temperature in a qualitative agreement with experiment.


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