Energy-Momentum Properties and the Spin of Short-Lived Particles

The space–time translation property of a stable particle is characterized by a time-like Lorentz vector (E, _k ). We show in this contribution that unstable particles are, in addition, characterized by a space-like Lorentz 4-vector of uncertainties, or spreads, ( E, k). This is true for unstable states created in formation-, in production-, and in decay-experiments. The space-like nature of the spread vector causes a nonzero momentum spread to be present in all Lorentz frames so that there is no Lorentz frame in which the unstable particle is entirely at rest. With the space-like spreadvector ( E, k) in addition to the time-like (E, _k ), also the rotation property of an unstable particle is affected, and unstable states have an uncertainty in their spin. This means neighboring spin states are occupied in addition to the original spin. Experiments are discussed that show a principal limitation of the accuracy of spin measurement from finite lifetimes. Wave functions for unstable particles are discussed, and we show in the example of a short-lived spin-0 state that the appearance of a spin neighbor in the amplitude is proportional to the inverse lifetime.     

Complex geometry,unification, and quantum gravity. II. The generations problem

The new model of elementary particles as vertical vectors on the principal fiber bundleU(3, 2) U(3, 2)/U(3, 1)×U(1) introduced in Part I is extended to higher generations.     

Hierarchy of symmetry breakings and neutral currents in anSU(6) grand unification model

In anSU(6) grand unification model with eight quarks and eight leptons belonging to 15-plet and singlet representations, the symmetry is spontaneously broken by the sequenceSU(6)SU(3) ^c ×SU(2)×U(1)×U(1)SU(3) ^c ×U(1). Fror two cases of symmetry breakings the effective weak neutral current coupling constants are compared with experiment. For theSU(3) ^c ×SU(2)×U(1)×U(1)×SU(3) ^c ×U(1) symmetry breaking, the coupling constants reproduce the Weinberg-Salam model with a small correction term. Agreement with the experimental mean values is improved with the correction term. Parity violation in atomic physics is also discussed.     

Thermodynamics of a spin 1/2 Anderson impurity in theU→∞ limit

The Bethe-ansatz equations describing the thermodynamics of the non-degenerate Anderson model are derived in theU limit (double occupation of the localized level is excluded). The set of Bethe-ansatz equations for theU limit is considerably different from the one for the finiteU case. The Kondo limit, the Fermi liquid behavior at lowT and the highT perturbation expansion for the thermodynamic potential are extracted from these equations.Heisenberg-fellow of the Deutsche Forschungsgemeinschaft     

Collision Integrals for Attractive Potentials

Motivated by previous discussions of particle interactions under the Manev potential U(r)=–/r–/r ², we construct the collision integrals for attractive potentials U(r) satisfying the condition U(r) r ²– as r0 with 0. For =0, we obtain a Boltzmann-type integral with a collision law allowing spiral interactions and nonunique correspondence between impact parameter and scattering angle. For >0, an additional Smoluchowski-type coagulation integral arises. All these integrals are derived and possible applications are discussed.     

Experimental study of cw carbon monoxide flame chemical laser of the CS2/O2/CO2 type

The performance of a continuous-wave (cw) CO flame chemical laser (FCL) of the CS₂/O₂/CO₂ type is presented. The laser gives up to 0.7 W cw output power on a number ofP _v (J) lines corresponding to 1110, ..., 76 vibrational bands of CO molecule. The measured values of chemical efficiency based on the reaction O+CSCO^*(v)+S and the specific power are 0.1% and 0.7J/g, respectively. The spectral composition of the CO FCL of the CS₂/O₂/CO₂ type shows lasing in the region from 5.194 to 5.573 m. All experimental measurements are conducted with a nondispersive optical cavity.     

Martensitic transformations in Ti (Ni,Fe) alloys

In this work we used x-ray structural analysis to investigate the martensitic transformations (MTs)B2R andRB19 in Ti(Ni, Fe) alloys containing 1, 2.5, 4, 5 at. % Fe, and the effect of heat treatment on the MT temperatures and sequence. In the majority of cases, it was found that the MTB2R proceeds through a two-phase region (+R). Heat treatment leads to a narrowing of the temperature interval of the existence of the two-phase region, weakly affects the onset temperatures of the MTsB2R T_R andRB19 M_s, and sharply increases the temperature-of the end of the MT M_e. The existence of the two-phase region is related to the two MT channelsB2R andB2B19 initially intrinsic to the allovs of the given compositions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 19–22, December, 1989.     

The structure of projection-valued states: A generalization of Wigner's theorem

A projection-valued state is defined to be a completely orthoadditive map from the projections on one Hilbert space into the projections on another Hilbert space, which preserves the unit. Any such mapping is shown to have the formP U ₁(P 1₁)U ₁ ^–1 U ₂(P 1₂)U ₂ ^–1 , whereU ₁ is unitary andU ₂ is antiunitary, generalizing Wigner's theorem on symmetry transformations. A physical interpretation is given and the relation to quantum logic is discussed.The contents of this paper are a portion of the author's dissertation at the University of Massachusetts at Amherst.     

Periodic nonlinear waves on a half-line

Nontrivial solutions of the equationu _tt=u _xx–g(u) which are 2-periodic int and which decay asx are shown to exist ifg(a)=0 andg(0)>1. Breather-like solutions, which also decay asx –, can be interpreted as homoclinic solutions in thex-dynamics; their existence is still in question for generalg.     

Mean field theory for Coulomb systems

We study a classical charge symmetric system with an external charge distributionq in three dimensions in the limit that the plasma parameter zero. We prove that ifq is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean field(x) where is given by-+ 2z sinh() =q This is the mean field equation of Debye and Hückel. The proof uses the sine-Gordon transformation, the Mayer expansion, and a correlation inequality.Work partially supported by NSF Grant MCS 82-02115.     

Symmetries of physical theories

A physical theory is, by definition, a complete orthomodular atomic lattice having the covering property. GivenL a quantum logic andS _L the set of all its states, a theorem is proved which asserts that, if certain reasonable assumptions concerningS _L are satisfied, then for any bijective convex mappingU: S _LS_L, satisfying also certain physically meaningful conditions, there exists a unique automorphismV: L L such thatU(p)=p oV ^–1 for allp S _L.     

Scalar particle with polarizability in a uniform external magnetic field

The model of a scalar structured particle is considered, which possesses polarizability in an external electromagnetic field. The expression for the 4-dimensional current density is found. The exact solution of the equations describing a scalar particle with polarizability in a uniform external magnetic field is obtained. Up to the terms of order O(H²), the energy spectrum can be formally obtained by the substitution of the particle mass in the expression for a pointlike scalar particle: mm–H²/2, where is the magnetic polarizability of the particle. It is shown that the rms radius of a trajectory can be obtained by the substitution of the charge in the well-known formula for a structureless scalar particle: ee(1{-H²/m)^1/2 (where is the electric polarizability).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 91–94, January, 1991.I thank A. I. L'vov for discussions.     

Complex geometry,unification, and quantum gravity. I. The geometry of elementary particles

The Poincaré group is replaced byU(3, 2), the pseudounitary extension of the de Sitter groupSO(3, 2), as internal and space-time symmetries are combined in a geometric setting which invalidates the no-go theorems. A new model of elementary particles as vertical vectors on the principal fiber bundleU(3, 2) U(3, 2)/U(3, 1)×U(1) is introduced and their interactions via Lie bracket analyzed. The model accounts for the four known superselection rules: spin, electric charge, baryon number, and lepton number.     

Solutions of the Maxwell and Yang-Mills equations associated with hopf fibrings

It is shown that the magnetic pole of lowest strength and the pseudoparticle solution of the Yang-Mills equations correspond to natural connections defined on the principal bundlesU(2)/U(1)=S ₃ S ₂ andSp(2)/Sp(1)=S ₇ S ₄, respectively. This observation leads to a general methods of constructing new, topologically nontrivial solutions of the Maxwell and Yang-Mills equations. Among them is an electromagnetic instanton defined over the two-dimensional complex projective space endowed with the Fubini-Study metric.On leave from the Institute of Theoretical Physics, Warsaw University, Hoza 69, Warsaw, Poland.     

Magnetooptic measurements on ultrathin Gd films on Y

We report on magnetooptic measurements on thin Gd films (3 Åd _Gd 1000 Å) grown on an y buffer layer and covered with a 100-Å Y protective top layer. Measurements were carried out in the temperature range from 2 to 300 K and for magnetic field up to 0.3 T. The effect of different growth conditions on the magnetic properties was examined. For films prepared at 300°C, ferromagnetic phase transitions have been observed for nominal film thicknesses down to about one monolayer of Gd. The thickness dependence of the Curie temperatureT _C follows a power law with an exponent =1.6 close to the theoretical value for a 3D-Ising ferromagnet.     

A two dimensional Lagrangian model with extended supersymmetry and infinitely many constants of motion

The reduction of the supersymmetric gradedSU(2|1) /S(U ₂×U ₁) -model is discussed. If no extra constraint is imposed, one gets a set of two coupled equations (involving two scalar superfields) which generalizes the supersymmetric sine-Gordon equation. It is shown that these equations, which can be derived by a supersymmetric Lagrangian, reproduce in the bosonic limit the reduced version of theO(4) -model (Pohlmeyer, Lund Regge, Getmanov model). Moreover the associate linear set and an infinite set of local conservation laws for this new supersymmetric model are exhibited. It turns out that, beyond the spinorial charge which generates the supersymmetry transformations, another unexpected spinorial charge is conserved; then the model appears to be invariant underN=2 extended supersymmetry.     

TheK S 0 →π0 l + l − andK L 0 →π0 l + l − decays in the standard model and the extended Nambu-Jona-Lasinio model

TheK _S ^{0 0} l ⁺ l ^– andK _L ^{0 0} l ⁺ l ^– decays are considered within the framework of the Standard model in the one-photon exchange approximation, i.e.K _S,L ^{0 0}+ *⁰ +l ⁺ l ^–. To evaluate the low-energy matrix elements of theK ⁰(¯K ⁰)⁰+ * transitions, the constituentquark-loop approximation, based on the extended Nambu-Jona-Lasino (NJL) model, is used. The obtained results are compared with other theoretical estimates and the experimental bounds.     

A spontaneously broken quintet Baryon model for strong interactions

A gauge type model of quantum field theory for strong interactions based on a quinted of observed fields, namely the proton, neutron, , _c and _b baryon fields is proposed. Gauging the resulting global symmetry groupK= SU(3)×¹ U(1)ײ U(1)׳ U(1) for matter fields, one obtains boson-fermion field theory with eleven gauge bosons. The analysis of admissible Higgs sector indicates that the Higgs multiple consists of one adjoint and two fundamental representationsSU(3) and three scalar representations of¹ U(1),² U(1) and³ U(1). The structure of the Higgs sector implies that the original symmetry group extends to the groupK×U(2). Breaking spontaneously the obtained field theory, one converts gauge bosons into the eleven massive vector bosons which can be identified with the observed , K^*, ¯K^*, , , J/ and Y vector mesons. The surviving global symmetry is isomorphic with the symmetry groupSU(2)× ⁰ U(1)× ×¹ U(1)ײ U(1)׳ U(1) corresponding to the isospin, strangeness, baryon number, charm and beauty conservation observed in strong interactions. The surviving Higgs scalars have the same quantum numbers as , K, ¯K, , S, , , and _b mesons. The model gives a newSU(3) classification scheme for baryons without charm and beauty in terms of triplets, sextets and 15-plets. These multiplets can be identified with the observed baryons; the scheme also includes the observed Z₀ and Z₁ baryons (the experimental evidence of which is, nevertheless, still weak). The model predicts the existence and the specific quantum numbers of new mesons and baryons with charm and beauty, and provides a very simple framework for the dibaryon analysis. Since all final physical fields are massive, this model is free from infrared divergences.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Fluctuation of the free energy in the Hopfield model

We prove that in the ergodic region [T>J ²(1 + r)] the deviation of the total free energy of the Hopfield neural network converges in distribution asN to a (shifted) Gaussian variable. Moreover, the free energy per site converges in probability to lim(1/N)ln _N .