Interpretation of Quantum Nonlocality by Conformal Quantum Geometrodynamics

The principles and methods of the Conformal Quantum Geometrodynamics (CQG) based on the Weyl’s differential geometry are presented. The theory applied to the case of the relativistic single quantum spin \(\frac{1}{2}\) leads a novel and unconventional derivation of Dirac’s equation. The further extension of the theory to the case of two spins \(\frac{1}{2}\) in EPR entangled state and to the related violation of Bell’s inequalities leads, by a non relativistic analysis, to an insightful resolution of the enigma implied by quantum nonlocality.     

Photon Asymmetries in {nd\rightarrow} 3 Hγ Using EFT({/\!\!\!\pi}) Approach

The parity-violating Lagrangian of the weak nucleon-nucleon (NN) interaction in the pionless effective field theory (EFT( \({/\!\!\!\pi}\) )) approach contains five independent unknown low-energy coupling constants (LECs). The photon asymmetry with respect to neutron polarization in \({np\rightarrow d\gamma A_\gamma^{np}}\) , the circular polarization of outgoing photon in \({np\rightarrow d\gamma P_\gamma^{np}}\) , the neutron spin rotation in hydrogen \({\frac{1}{\rho}\frac{d\phi^{np}}{dl}}\) , the neutron spin rotation in deuterium \({\frac{1}{\rho}\frac{d\phi^{nd}}{dl}}\) and the circular polarization of γ-emission in \({nd\rightarrow}\) ³ Hγ \({P^{nd}_\gamma}\) are the parity-violating observables which have been recently calculated in terms of parity-violating LECs in the EFT( \({/\!\!\!\pi}\) ) framework. We obtain the LECs by matching the parity-violating observables to the Desplanques, Donoghue, and Holstein (DDH) best value estimates. Then, we evaluate photon asymmetry with respect to the neutron polarization \({a^{nd}_\gamma}\) and the photon asymmetry in relation to deuteron polarization \({A^{nd}_\gamma}\) in \({nd\rightarrow}\) ³ Hγ process. We finally compare our EFT( \({/\!\!\!\pi}\) ) photon asymmetries results with the experimental values and the previous calculations based on the DDH model.     

Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field h. Using ideas from dynamical systems and functional analysis, we show that the free energy f in the vicinity of the second-order phase transition is given, exactly, by $$f\sim\frac{t}{\log t}-\frac{1}{2}\frac{h^2}{t}\quad\mbox{for }h^2\ll t\ll1.$$ Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_{c}})$ is a reduced temperature, so that the deviation from the critical point is scaled by the Lyapunov exponent of the Gauss map, λ _G . It follows that λ _G determines the amplitude of both the specific heat and susceptibility singularities. To our knowledge, there is only one other microscopically defined interacting model for which the free energy near a phase transition is known as a function of two variables. Our results confirm what was found previously with a cluster approximation, and show that a clustering mechanism is in fact responsible for the transition. However, the results disagree in part with a renormalisation group treatment.     

Analytic Binding Energies for Two-Baryon Bound States in 2 + 1 Strongly Coupled Lattice QCD With Two-Flavors

We consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 × 2 spin matrices. An imaginary time functional integral formulation with Wilson’s action is used in the strong coupling regime, i.e. small hopping parameter ${0 < \kappa \ll 1}$ , and much smaller plaquette coupling ${\beta, 0 < \beta \ll \kappa}$ . In this regime, it is known that the low-lying energy-momentum spectrum contains isolated dispersion curves identified with baryons and mesons with asymptotic masses ${m\approx-3\ln\kappa}$ and ${m_m\approx-2\ln\kappa}$ , respectively. We prove the existence of two (labelled by ±) two-baryon bound states for each of the total isospin sectors I = 0,1 and we obtain, in each case, the exact binding energies ${\epsilon_{I\,\pm} }$ (of order ${\kappa^2}$ ) which extend to jointly analytic function in ${\kappa}$ and β. We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for ${\alpha_0=\frac 14, \alpha_1=\frac 1{12}, \alpha_2=\frac12, \alpha_3=\frac 34}$ and small ${\delta >0 }$ , that the bound state masses ${2m-\epsilon_{I\,\pm}}$ are the only points in the mass spectrum in ${(0,2m-\epsilon_{I\,\pm}+\delta \alpha_I\kappa^2)}$ , for I = 0,1, and in ${(0,2m-(1+\delta)\alpha_I\kappa^2)}$ , for I = 2,3. These results are exact and validate our previous results obtained in a ladder approximation. The method employs suitable two- and four-point correlations with spectral representations and a lattice Bethe-Salpeter equation. For I = 0,1, a quark, antiquark space-range one potential of order ${\kappa^2}$ is found to be the dominant contribution to the two-baryon interaction and the interaction of the individual quark isospins of one baryon with those of the other is described by permanents. A novel spectral free decomposition (but spectral representation motivated, for real κ and β) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy.     

Suppressed Dispersion for a Randomly Kicked Quantum Particle in a Dirac Comb

I study a model for a massive one-dimensional particle in a singular periodic potential that is receiving kicks from a gas. The model is described by a Lindblad equation in which the Hamiltonian is a Schrödinger operator with a periodic δ-potential and the noise has a frictionless form arising in a Brownian limit. I prove that an emergent Markov process in an adiabatic limit governs the momentum distribution in the extended-zone scheme. The main result is a central limit theorem for a time integral of the momentum process, which is closely related to the particle’s position. When normalized by $t^{\frac{5}{4}}$ the integral process converges to a time-changed Brownian motion whose diffusion rate depends on the momentum process. The scaling $t^{\frac{5}{4}}$ contrasts with $t^{\frac{3}{2}}$ , which would be expected for the case of a smooth periodic potential or for a comparable classical process. The difference is a wave effect driven by momentum reflections that occur when the particle’s momentum is kicked near the half-spaced reciprocal lattice of the potential.     

Random Field Induced Order in Low Dimension I

Consider the classical XY model in a weak random external field pointing along the Y axis with strength ${\epsilon}$ . We prove that the model defined on ${\mathbb{Z}^3}$ with nearest neighbor coupling exhibits residual magnetic order in the horizontal direction for arbitrarily weak random field strengths and, depending on field strength, sufficiently low temperature.     

Spin Symmetry in the Relativistic q-Deformed Morse Potential

In this paper, we investigate the spin symmetry case of a spin ${-\frac{1}{2}}$ particle governed by a q-deformed Morse potential by presenting an approximate bound-state solutions of the Dirac equation with the spin-orbit coupling term for spin symmetry vector and scalar q-deformed Morse potential within framework of the Pekeris approximation. The relativistic energy levels are obtained using the Nikiforov–Uvarov (NU) method and the two-components spinor wave functions are obtain in terms of the Jacobi polynomials. It is found that there exist only positive-energy for the bound states of some diatomic molecules under spin symmetry.     

K-conversion coefficient of the 53.3 keV transition and\frac{K}{{L + M}}-ratio of the 13.34 keV transition in73Ge

TheK-conversion coefficient of the 53.3 keV transition in⁷³Ge was measured by coincidence techniques to be αk ₁=7.1 ± 0.6 indicating very good agreement with heory forM2-radiation. The \(\frac{K}{{L + M}}\) -ratio of the 13.34 keV transition to the ground state was determined using the same techniques. The resulting value \(\left( {\frac{K}{{L + M}}} \right)_2 \) =0.36 ± 0.03 supports theE2-character of this radiation and therefore a spin assignment of \(\frac{5}{2}\) for the 13.34 keV level. The measured lifetime of this transition (T _1,2=(2.95 ± 0.05) μsec) corresponds to a factor of 15 greater than the Weisskopf estimation for a pureE2-transition. A short discussion of a possible transfer of the collectivity of the⁷²Ge-nucleus to the⁷³Ge-nucleus is given.     

Harmonic Oscillator Trap and the Phase-Shift Approximation

The energy-spectrum of two point-like particles interacting in a 3-D isotropic Harmonic Oscillator (H.O.) trap is related to the free scattering phase-shifts \(\delta \) of the particles by a formula first published by Busch et al. It is here used to find an expression for the shift of the energy levels, caused by the interaction, rather than the perturbed spectrum itself. In the limit of high energy (large quantum number \(n\) of the H.O.) this shift (in H.O. units) is shown to be given by \(\Delta =-2\frac{\delta }{\pi }\) , also exact in the limit of infinite scattering length ( \(\delta =\pm \frac{\pi }{2}\) ) in which case \(\Delta =\mp 1\) . Numerical investigation shows that this expression otherwise differs from the exact result of Busch et al., by less than \(\frac{1}{2}\,\%\) except for \(n=0\) when it can be as large as \(\approx \) 2.5 %. This result for the energy-shift is well known from another exactly solvable model, namely that of two particles interacting in a spherical infinite square-well trap (or box) of radius \(R\) in the limit \(R\rightarrow \infty \) , and/or in the limit of large energy. It is in solid state physics referred to as Fumi’s theorem. It can be (and has been) used in (infinite) nuclear matter calculations to calculate the two-body effective interaction in situations where in-medium effects can be neglected. It is in this context referred to as the phase-shift approximation a term also used throughout this report.     

Analysis of the \frac{1} {2}^ - and \frac{3} {2}^ - heavy and doubly heavy baryon states with QCD sum rules

In this article, we study the $\frac{1} {2}^ -$ and $\frac{3} {2}^ -$ heavy and doubly heavy baryon states $\Sigma _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi '_Q \left( {\frac{1} {2}^ - } \right)$ , $\Omega _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Omega _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Sigma _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Omega _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ and $\Omega _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ by subtracting the contributions from the corresponding $\frac{1} {2}^ +$ and $\frac{3} {2}^ +$ heavy and doubly heavy baryon states with the QCD sum rules in a systematic way, and make reasonable predictions for their masses.     

Study of spin-wave dynamics in Fe65Ni35 ferromagnetic via small-angle polarized-neutron scattering

The results of studying the spin dynamics of a classical Fe₆₅Ni₃₅ invar alloy are presented and analyzed. The investigations are performed via small-angle polarized-neutron scattering in the oblique geometry of a magnetic field at various temperatures (T < T _C). This approach is based on the analysis of left-right asymmetry in the magnetic scattering of polarized neutrons. The asymmetry effect arises when the magnetization direction of a sample is inclined with respect to the wave vector of the incident beam. The spin-wave scattering is concentrated within a range bounded by the cutoff angle θ_c determined by the magnetic field: θ _c ² (H) = θ ₀ ² ?(gμ_B H)θ₀/E, where \(\theta _0 = \hbar ^2 \frac{1} {{2Dm_n }}\) , H is the external magnetic field, E is the initial neutron energy, D is the spin-wave stiffness constant, and m _n is the neutron mass. The scattering is blurred by spinwave damping in the vicinity of the cutoff angle. The spin-wave stiffness constant can be obtained from a comparison of the asymmetric contribution to scattering and a model function. The temperature dependence D = D(T) is well defined by the expression D = D ₀ |τ| ^x , where \(\tau = 1 - \frac{T} {{T_C }}\) , x = 0.47 ± 0.01, D ₀ = 137 ± 3 meVŲ, and τ > 0.1 in the entire temperature range. The given method enables us to construct the temperature dependence of the spin-wave stiffness constant with a high accuracy and a small step.     

Tail Asymptotics of Free Path Lengths for the Periodic Lorentz Process: On Dettmann’s Geometric Conjectures

In the simplest case, consider a \({\mathbb{Z}^d}\) -periodic (d ≥ 3) arrangement of balls of radii < 1/2, and select a random direction and point (outside the balls). According to Dettmann’s first conjecture, the probability that the so determined free flight (until the first hitting of a ball) is larger than t >  > 1 is \({\sim\frac{C}{t}}\) , where C is explicitly given by the geometry of the model. In its simplest form, Dettmann’s second conjecture is related to the previous case with tangent balls (of radii 1/2). The conjectures are established in a more general setup: for \({\mathcal{L}}\) -periodic configuration of—possibly intersecting—convex bodies with \({\mathcal{L}}\) being a non-degenerate lattice. These questions are related to Pólya’s visibility problem (Arch Math Phys Ser 2:135–142, 1918), to theories of Bourgain et al. (Commun Math Phys 190:491–508,1998), and of Marklof–Strömbergsson (Ann Math 172:1949–2033,2010). The results also provide the asymptotic covariance of the periodic Lorentz process assuming it has a limit in the super-diffusive scaling, a fact if d = 2 and the horizon is infinite.     

LRS Bianchi Type II Massive String Cosmological Model for Stiff Fluid Distribution with Decaying Vacuum Energy (Λ)

An LRS Bianchi Type II model formed by massive strings with decaying vacuum energy (Λ) for stiff fluid distribution is studied in the context of general relativity. To get the deterministic model, we have assumed that $\frac{\sigma}{\theta} =\mathrm{constant}$ where σ is shear and θ the expansion in the model and decaying vacuum energy (Λ) is proportional to H ² (H is Hubble parameter) as used in Arbab (Gen. Relativ. Gravit. 29:51, 1997). We find that the model represents decelerating and accelerating phases of universe. The decaying vacuum energy (Λ) is proportional to $\frac{1}{\tau^{2}}$ as obtained by Bertolami (Nuovo Cimento B 93:36, 1986) and Hubble parameter is proportional to $\frac{1}{\tau}$ which matches with the observation. The model in general represents anisotropic space-time. However, in special case, it isotropizes. The particle density (ρ _p ) and string tenson (λ) are initially large but decrease due to lapse of time. The model also admits particle horizon and entropy is inversely proportional absolute temperature. Thus the model is in good agreement with present age of universe.     

Light quark masses in quantum chromodynamics and chiral symmetry breaking

We derive model independent lower bounds for the sums of effective quark masses \(\bar m_u + \bar m_d \) and \(\bar m_u + \bar m_s \) . The bounds follow from the combination of the spectral representation properties of the hadronic axial currents two-point functions and their behavior in the deep euclidean region (known from a perturbative QCD calculation to two loops and the leading non-perturbative contribution). The bounds incorporate PCAC in the Nambu-Goldstone version. If we define the invariant masses \(\hat m\) by $$\bar m_i = \hat m_i \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^{{{\gamma _1 } \mathord{\left/ {\vphantom {{\gamma _1 } {\beta _1 }}} \right. \kern-\nulldelimiterspace} {\beta _1 }}} $$ and <F ²> is the vacuum expectation value of $$F^2 = \Sigma _a F_{(a)}^{\mu v} F_{\mu v(a)} $$ , we find, e.g., $$\hat m_u + \hat m_d \geqq \sqrt {\frac{{2\pi }}{3} \cdot \frac{{8f_\pi m_\pi ^2 }}{{3\left\langle {\alpha _s F^2 } \right\rangle ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }}} $$ ; with the value <α _u F ²?0.04GeV⁴, recently suggested by various analysis, this gives $$\hat m_u + \hat m_d \geqq 35MeV$$ . The corresponding bounds on \(\bar m_u + \bar m_s \) are obtained replacingm _π ² f _π bym _K ² f _K . The PCAC relation can be inverted, and we get upper bounds on the spontaneous masses, \(\hat \mu \) : $$\hat \mu \leqq 170MeV$$ where \(\hat \mu \) is defined by $$\left\langle {\bar \psi \psi } \right\rangle \left( {Q^2 } \right) = \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^d \hat \mu ^3 ,d = {{12} \mathord{\left/ {\vphantom {{12} {\left( {33 - 2n_f } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {33 - 2n_f } \right)}}$$ .     

Three-loop relation of quark\overline {MS} and pole masses

We calculate, exactly, the next-to-leading correction to the relation between the \(\overline {MS} \) quark mass, \(\bar m\) , and the scheme-independent pole mass,M, and obtain $$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$ as an accurate approximation forN _F?1 light quarks of massesM _i <M. Combining this new result with known three-loop results for \(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the \(\overline {MS} \) mass, \(\bar m\) (μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom \(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections.     

Simulating spin-\frac{3}{2} particles at colliders

Support for interactions of spin- $\frac{3}{2}$ particles is implemented in the FeynRules and ALOHA packages and tested with the MadGraph 5 and CalcHEP event generators in the context of three phenomenological applications. In the first, we implement a spin- $\frac{3}{2}$ Majorana gravitino field, as in local supersymmetric models, and study gravitino and gluino pair-production. In the second, a spin- $\frac{3}{2}$ Dirac top-quark excitation, inspired from compositeness models, is implemented. We then investigate both top-quark excitation and top-quark pair-production. In the third, a general effective operator for a spin- $\frac{3}{2}$ Dirac quark excitation is implemented, followed by a calculation of the angular distribution of the s-channel production mechanism.     

Liouville-Type Theorems for the Forced Euler Equations and the Navier–Stokes Equations

In this paper we study the Liouville-type properties for solutions to the steady incompressible Euler equations with forces in ${\mathbb {R}^N}$ . If we assume “single signedness condition” on the force, then we can show that a ${C^1 (\mathbb {R}^N)}$ solution (v, p) with ${|v|^2+ |p| \in L^{\frac{q}{2}}(\mathbb {R}^N),\,q \in (\frac{3N}{N-1}, \infty)}$ is trivial, v = 0. For the solution of the steady Navier–Stokes equations, satisfying ${v(x) \to 0}$ as ${|x| \to \infty}$ , the condition ${\int_{\mathbb {R}^3} |\Delta v|^{\frac{6}{5}} dx < \infty}$ , which is stronger than the important D-condition, ${\int_{\mathbb {R}^3} |\nabla v|^2 dx < \infty}$ , but both having the same scaling property, implies that v = 0. In the appendix we reprove Theorem 1.1 (Chae, Commun Math Phys 273:203–215, 2007), using the self-similar Euler equations directly.