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L. P. Horwitz

Publications and source records attributed to L. P. Horwitz.

At least 73 records · Page 4Linked to original sources
arXiv1997

New Mass Relations for Heavy Quarkonia

By assuming the existence of (quasi)-linear Regge trajectories for heavy quarkonia in the low energy region, we derive a new, sixth power, meson mass relation which shows good agreement with experiment for both charmed and beauty mesons. This relation may be reduced to a quadratic Gell-Mann-Okubo type formula by fitting the values of the Regge slopes of these (quasi)-linear trajectories. For charmed mesons, such a formula holds with an accuracy of $\sim 1$%, and is in qualitative agreement with the relation obtained previously by the application of the linear spectrum to a meson hexadecuplet.

hep-ph↗
arXiv1997

Schwinger Algebra for Quaternionic Quantum Mechanics

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \to \infty$.

hep-th↗
arXiv1996

Lax-Phillips Theory and Quantum Evolution

The scattering theory of Lax and Phillips, designed primarily for hyperbolic systems, such as electromagnetic or acoustic waves, is described. This theory provides a realization of the theorem of Foias and Nagy; there is a subspace of the Hilbert space in which the unitary evolution of the system, restricted to this subspace, is realized as a semigroup. The embedding of the quantum theory into this structure, carried out by Flesia and Piron, is reviewed. We show how the density matrix for an effectively pure state can evolve to an effectively mixed state (decoherence) in this framework. Necessary conditions are given for the realization of the relation between the spectrum of the generator of the semigroup and the singularities of the $S$-matrix (in energy representation). It is shown that these conditions may be met in the Liouville space formulation of quantum evolution, and in the Hilbert space of relativistic quantum theory.

quant-ph↗
arXiv1996

On the Thermodynamics of Chiral Symmetry Restoration

The formulas for the temperature dependences of the non-strange and strange quark condensates are derived by taking into account the contribution of the massive resonances. Critical temperature of the chiral symmetry restoration transition is established to be 190 MeV if only meson resonances are considered, and 175 MeV if both meson and baryon resonances are taken into account.

hep-ph↗
arXiv1996

Mass Spectrum of a Meson Nonet is Linear

It is argued that the mass spectrum of a meson nonet is linear, consistent with the standard Gell-Mann--Okubo mass formula and leading to an extra Gell-Mann--Okubo mass relation for the masses of the isoscalar states. This relation is shown to hold with an accuracy of up to $\sim $3\% for all well-established nonets. It also suggests a new $q\bar{q}$ assignment for the scalar meson nonet.

hep-ph↗
arXiv1996

Mass Spectrum of a Baryon Octet is Linear

It is argued that the mass spectrum of a baryon octet is linear, consistent with a Gell-Mann--Okubo type relation for the squared masses of the baryons obtained previously by Balázs and Nicolescu. The mass spectrum of a baryon decuplet is briefly discussed.

hep-ph↗
arXiv1996

Gell-Mann--Okubo Mass Formula for an SU(4) Meson Hexadecuplet

Using a linear mass spectrum of an $SU(4)$ meson hexadecuplet, we derive the Gell-Mann--Okubo mass formula for the charmed mesons, in good agreement with experiment. Possible generalization of this method to a higher symmetry group is briefly discussed.

hep-ph↗
arXiv1996

On the Thermodynamics of Hot Hadronic Matter

The equation of state of hot hadronic matter is obtained, by taking into account the contribution of the massive states with the help of the resonance spectrum $τ(m)\sim m^3$ justified by the authors in previous papers. This equation of state is in agreement with that provided by the low-temperature expansion for the pion intracting gas. It is shown that in this picture the deconfinement phase transition is absent, in agreement with lattice gauge calculations which show the only phase transition of chiral symmetry restoration. The latter is modelled with the help of the restriction of the number of the effective degrees of freedom in the hadron phase to that of the microscopic degrees of freedom in the quark-gluon phase, through the corresponding truncation of the hadronic resonance spectrum, and the decrease of the effective hadron masses with temperature, predicted by Brown and Rho. The results are in agreement with lattice gauge data and show a smooth crossover in the thermodynamic variables in a temperature range $\sim 50$ MeV.

hep-ph↗
arXiv1996

A Chiral Spin Theory in the Framework of an Invariant Evolution Parameter Formalism

We present a formulation for the construction of first order equations which describe particles with spin, in the context of a manifestly covariant relativistic theory governed by an invariant evolution parameter; one obtains a consistent quantized formalism dealing with off-shell particles with spin. Our basic requirement is that the second order equation in the theory is of the Schrödinger-Stueckelberg type, which exhibits features of both the Klein-Gordon and Schrödinger equations. This requirement restricts the structure of the first order equation, in particular, to a chiral form. One thus obtains, in a natural way, a theory of chiral form for massive particles, which may contain both left and right chiralities, or just one of them. We observe that by iterating the first order system, we are able to obtain second order forms containing the transverse and longitudinal momentum relative to a time-like vector $t_μt^μ=-1$ used to maintain covariance of the theory. This time-like vector coincides with the one used by Horwitz, Piron, and Reuse to obtain an invariant positive definite space-time scalar product, which permits the construction of an induced representation for states of a particle with spin. We discuss the currents and continuity equations, and show that these equations of motion and their currents are closely related to the spin and convection parts of the Gordon decomposition of the Dirac current. The transverse and longitudinal aspects of the particle are complementary, and can be treated in a unified manner using a tensor product Hilbert space. Introducing the electromagnetic field we find an equation which gives rise to the correct gyromagnetic ratio, and is fully Hermitian under the proposed scalar product. Finally, we show that the original structure of Dirac's

hep-th↗
arXiv1996

Microcanonical Ensemble and Algebra of Conserved Generators for Generalized Quantum Dynamics

It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a statistical approximation to an underlying generalized quantum dynamics. This result was obtained by an argument based on a Ward identity analogous to the equipartition theorem of classical statistical mechanics. We construct here a microcanonical ensemble which forms the basis of this canonical ensemble. This construction enables us to define the microcanonical entropy and free energy of the field configuration of the equilibrium distribution and to study the stability of the canonical ensemble. We also study the algebraic structure of the conserved generators from which the microcanonical and canonical ensembles are constructed, and the flows they induce on the phase space.

hep-th↗
arXiv1996

Hadronic Resonance Spectrum May Help in Resolution of Meson Nonet Enigmas

The identification of problematic meson states as the members of the quark model $q\bar{q}$ nonets by using a hadronic resonance spectrum is discussed. The results favor the currently adopted $q\bar{q}$ assignments for the axial-vector, tensor, and 1 $^3F_4$ $J^{PC}=4^{++}$ meson nonets, and suggest a new $q\bar{q}$ assignment for the scalar meson nonet which favors the interpretation of the $f_0(980)$ and $f_0(1710)$ mesons as non-$q\bar{q}$ objects. We also suggest that the 2 $^3S_1$ $\frac{1}{2}(1^{-})$ state should be identified with the $K^\ast (1680)$ rather than $K^\ast (1410)$ meson.

hep-ph↗
arXiv1996

Construction of a Complete Set of States in Relativistic Scattering Theory

The space of physical states in relativistic scattering theory is constructed, using a rigorous version of the Dirac formalism, where the Hilbert space structure is extended to a Gel'fand triple. This extension enables the construction of ``a complete set of states'', the basic concept of the original Dirac formalism, also in the cases of unbounded operators and continuous spectra. We construct explicitly the Gel'fand triple and a complete set of ``plane waves'' -- momentum eigenstates -- using the group of space-time symmetries. This construction is used (in a separate article) to prove a generalization of the Coleman-Mandula theorem to higher dimension.

hep-th↗
arXiv1996

Generalization of the Coleman-Mandula Theorem to Higher Dimension

The Coleman-Mandula theorem, which states that space-time and internal symmetries cannot be combined in any but a trivial way, is generalized to an arbitrarily higher spacelike dimension. Prospects for further generalizations of the theorem (space-like representations, larger time-like dimension, infinite number of particle types) are also discussed. The original proof relied heavily on the Dirac formalism, which was not well defined mathematically at that time. The proof given here is based on the rigorous version of the Dirac formalism, based on the theory of distributions. This work serves also to demonstrate the suitability of this formalism for practical applications.

hep-th↗
arXiv1996

Complexity, Tunneling and Geometrical Symmetry

It is demonstrated in the context of the simple one-dimensional example of a barrier in an infinite well, that highly complex behavior of the time evolution of a wave function is associated with the almost degeneracy of levels in the process of tunneling. Degenerate conditions are obtained by shifting the position of the barrier. The complexity strength depends on the number of almost degenerate levels which depend on geometrical symmetry. The presence of complex behavior is studied to establish correlation with spectral degeneracy.

cond-mat↗
arXiv1996

Mass - Proper Time Uncertainty Relation in a Manifestly Covariant Relativistic Statistical Mechanics

We prove the uncertainty relation $T_{\triangle V}\triangle m\stackrel{>}{\sim }2π\hbar /c^2,$ which is realized on a statistical mechanical level for an ensemble of events in $(1+D)$-dimensional spacetime with motion parametrized by an invariant ``proper time'' $τ,$ where $T_{\triangle V}$ is the average passage interval in $τ$ for the events which pass through a small (typical) $(1+D)$-volume $\triangle V,$ and $\triangle m$ is the dispersion of mass around its on-shell value in such an ensemble. We show that a linear mass spectrum is a completely general property of a $(1+D)$-dimensional off-shell theory.

hep-th↗
arXiv1996

A New Relativistic High Temperature Bose-Einstein Condensation

We discuss the properties of an ideal relativistic gas of events possessing Bose-Einstein statistics. We find that the mass spectrum of such a system is bounded by $μ\leq m\leq 2M/μ_K,$ where $μ$ is the usual chemical potential, $M$ is an intrinsic dimensional scale parameter for the motion of an event in space-time, and $μ_K$ is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with nonzero chemical potential $μ,$ the mass spectrum is shown to be bounded by $|μ|\leq m\leq 2M/μ_K,$ and a special type of high-temperature Bose-Einstein condensation can occur. We study this Bose-Einstein condensation, and show that it corresponds to a phase transition from the sector of continuous relativistic mass distributions to a sector in which the boson mass distribution becomes sharp at a definite mass $M/μ_K.$ This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value.

hep-th↗