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An algebraically deformed three-dimensional harmonic oscillator is described. It is an exactly solvable quantum-dynamical system, although its coordinates as well as its momenta are non-Abelian. Nevertheless, its angular momentum generates the usual, non-deformed rotation group. A possibility of its infinite-dimensional generalisation towards a new, algebraically deformed boson field is sketched. For such a field a new phenomenon of energy-mode saturation may appear.

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The dependence of the angular decay distributions of particles (resonances) on the decay dynamics is discussed. The simplest cases, where this dynamics either is irrelevant, or affects only one constant parameter are described. A simple method of calculating the parameters entering the angular decay distribution is presented for the case, when the decay dynamics is known.

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Nonlinear relativistic field theory in 3 + 1 dimensions describing the dust of photons is outlined. This theory possesses an infinite hierarchy of conservation laws. It can be viewed as a limiting case of Born–Infeld nonlinear electrodynamics obtained when the critical field tends to zero, i.e., when all fields become overcritical.

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Relation of the intermittency phenomenon observed in spectra of particles produced in high-energy collisions to the intensity correlations between identical particles is discussed. It is argued that the compatibility of the two effects requires scale-invariant (power law) fluctuations of the sue of the interaction region.

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It is suggested that quasars and active galactic nuclei are small regions (droplets) of pseudo-vacuum, possibly containing matter, that decay into real vacuum and ordinary matter. In addition, the droplets may play a role in galaxy formation.

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We present a summary of the present status of efforts to solve the problem in which pairs are produced in a strong electric field, are accelerated by it, and then react back on it through the counter-field produced by their current. This picture has been used by Białas and Czyż and others as a model for effects that may possibly arise in the study of the quark-gluon plasma. We here give a didactic review of recent developments in this back-reaction problem. We first present a simple version of the theory of pair tunneling from a fixed electric field, and then sketch how this has been applied to the quark-gluon plasma. Then we turn to a field formulation of the problem for charged bosons, which leads to the need to carry out a renormalization program, outline d again in simple terms. Numerical results for this program are presented for one spatial dimension, the corresponding physical behavior of the system is discussed, and the implications for three spatial dimensions axe considered. We exhibit a phenomenological transport equation embodying physics that is essentially identical to that of the field formulation, thus helping to tie the model of Białas and Czyż for the quark-gluon plasma to a field-theory formulation. Last, we note the status of extensions to (i) the problem with three space dimensions; (ii) the fermion case; (iii) the formulation in terms of boost-invariant variables (as desirable for the quark-gluon plasma); and (iv) transport equations derived in a fundamental and consistent fashion.

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The quantized Coulomb field is decomposed into irreducible unitary representations of the proper, ortochronous Lorentz group. It is shown that for \(e^2/\hbar c \gt \pi \) the Coulomb field contains representations from the main series. For \(0 \lt e^2/\hbar c \lt \pi \) there is additionally a representation from the supplementary series corresponding to the special value of the Casimir operator \(-\frac {1}{2}M_{\mu \nu }M^{\mu \nu }=\frac {e^2}{\pi \hbar c}\left (2-\frac {e^2}{\pi \hbar c}\right )\).

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The effects of symmetry breaking in \(S\)-wave channels are discussed, attempting to illuminate the physics that distinguishes the \(S\)-wave channel. The importance of a centrifugal barrier in the other channels is emphasized. An overview of the origins of approximate symmetries, both among the light quarks and among the heavy quarks, is given in terms of quarks and their properties. Some new relations among weak decay matrix elements are obtained.

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Theoretical ideas concerning the Pomeron in perturbative QCD are reviewed. The Lipatov equation with asymptotic freedom effects taken into account is recalled and the corresponding spectrum of eigenvalues controlling the bare Pomeron intercept analysed. Possible phenomenological implications of the perturbative QCD Pomeron for deep inelastic scattering at the HERA ep collider are briefly discussed.

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The covariantly quantized momentum operator of the relativistic string in Minkowski space is redefined so that its domain is within the forward light cone. This leads, by definition, to a positive spectrum for the mass-squared operator.

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This note is written as a tribute to professor Wiesław Czyż on the occasion of his 65-th birthday. It is a variation on a paper (Acta Phys. Pol. B9, 433 (1978)) entitled “A quasi-classical description of isospin-conservation in multiparticle production”, written when he and his wife spent some time in Utrecht. In that paper the correlations between charged and neutral pions were calculated and expressed in terms of the average charge multiplicity and the charge dispersion. Similar calculations will be reported here, but now also K- and \(\eta \)-mesons will be included. Again the conservation law has a large effect on the multiplicity distribution of the particles produced in a high energy reaction.

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We review the question posed in the title, with emphasis on hard-collision phenomena utilizing rapidity gaps and jets as a diagnostic. If constituent quarks are very black, it is conceivable that various exotic phenomena exist, including production of strange matter, disoriented chiral condensate, and/or ultra-hot quark-gluon plasma.

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Quantum hadrodynantics (QHD) is the formulation of the relativistic nuclear many-body problem in terms of renormalizable quantum field theory based on hadronic degrees of freedom. A model with neutral scalar and vector mesons \((\sigma , \omega )\) has had significant phenomenological success (QHD—I). An extension to include the isovector \(\rho \) through a Yang–Mills local gauge theory based on isospin, with the vector meson mass generated through the Riggs mechanism, also exists (QHD—II). Pions can be incorporated in a chiral-invariant fashion using the linear sigma model. The low-mass scalar of QHD—I is then produced dynamically through \(\pi \pi \) interactions in this chiral-invariant theory. The question arises whether one can construct a chiral-invariant QHD Lagrangian that incorporates the minimal set of hadrons \(\{N, \omega , \pi , \rho \}\), where \(N = (^p_n)\) is the nucleon. These are the most important degrees of freedom for describing the low-energy nucleon–nucleon interaction and nuclear structure physics. In this paper we construct a chiral-invariant Yang–Mills theory based on the local gauge symmetry SU(2)\(_{\rm R} \times \) SU(2)\(_{\rm L}\). The baryon mass is generated through spontaneous symmetry breaking (as in the linear sigma model), and the vector meson masses are produced through the Riggs mechanism. The theory is parity conserving. Two baryon isodoublets with opposite hypercharge \(y\) are necessary to eliminate chiral anomalies. The minimal set of hadrons required consists of \(\{N, \Xi ; \sigma , \omega , \pi , \rho , a; \eta , \xi \}\) where \(a\) is the chiral partner of the \(\rho \) (the \(a\) naturally obtains a higher mass in the model), and the \(\eta \) and \(\xi \) represent scalar and pseudoscalar Riggs particles. The parameters in this minimal theory consist of eight coupling constants and one mass \((g_{\omega }, g_{0\pi } + yg_{1\pi }, g_{\rho }, \mu ^2_{\rm M}, \lambda _{\rm M}, \mu ^2_{\rm H}, \lambda _{\rm H}; m_{\omega })\), where \(\mu ^2\) and \(\lambda \) define the meson interaction potentials that lead to spontaneous symmetry breaking.

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An approximate method of deriving the energy of nuclear matter with an arbitrary momentum distribution from known ground state properties of nuclear matter is discussed. it is shown that for the momentum-dependent Skyrme effective interaction the method is exact.

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With the aid of two exactly solvable models, interference effects are shown to be important for the passage of a fast particle through a nucleus when time dilation increases the lifetime of the excited states of the incident particle sufficiently.

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The potential of an anisotropic harmonic oscillator rotated externally with constant frequency is employed for the investigation of the basis for the high spin spectra in the \(sd\)-shell nuclei. The analysis emphasizes the search for proper nucleonic configurations. Various physical effects typical for the yrast region in these nuclei are discussed.