Unitarity constraints for new physics induced by dim-6 operators

We compute the helicity amplitudes for bosonboson scattering at high energy due to the operatorsO _BΦ,O _WΦ andO _UB , and we derive the corresponding unitarity bounds. Thus, we provide relations between the couplings of these operators and the corresponding New Physics thresholds, where either unitarity is saturated or new degrees of freedom are excited. We compare the results with those previously obtained for the operatorsO _W andO _UW and we discuss their implications for direct and indirect tests at present and future colliders. The present treatment completes the study of the unitarity constraints for all blind bosonic operators.     

Origin of regge symmetry for wigner coefficients ofLU(2)

Using general properties of the representations of unitary groups and their relations to representations of symmetric groups, the 3j symbol of the unitary unimodular group ?U(2) is written in terms of a 9j symbol of the unitary unimodular group ?U(J) withJ being the sum of the threej's. The result yields the Regge symmetry of the 3j symbol as a consequence of new relations between Wigner coefficients and special invariants of unitary groups on one hand and the association symmetry of the symmetric group on the other.     

Entropic dimension for completely positive maps

We extend the concept of quantum dynamical entropyh _φ (γ) to cover the case of a completely positive map γ. Forh _φ (γ) = 0 we examine the limit $$h_\phi (N,\gamma ,\beta ) = \mathop {\lim }\limits_n (1/n^\beta )H_\phi (N,\gamma {\rm N},...,\gamma ^{n -- 1} N)$$ calling the turning point β₀ between zero and infiniteh _φ (N, γ, β) the “entropic dimension”D _N (γ). The application of this theory to a solvable irreversible quantum dynamical semigroup on a one-dimensional fermion lattice provides any value ofD _N (γ) between 0 and 1.     

Demonstration of the origins of cooperativity within SU2×L 6 mapping over\left\{ {I\tilde H_\upsilon } \right\} Liouvillian carrier subspaces characterising the MQ-NMR cluster [A]6(L 6) and its\{ |kq\upsilon :[\tilde \lambda ] > > \} tensorial bases

The fundamental mappings over carrier subspace and substructures associated with \(\{ |kq\upsilon > > \} \) augmented spin algebras of Liouville space, and their mapping onto a subduced symmetry, are derived for [A]₆(L ₆) spin clusters within the combinatorial context of Rota-Cayley algebra over a field. Use of suitable lexical sets of combinatorialp-tuples (number partitions) over {|IM(M ₁?M _n )>}M, followed by the subsequent use ofL _n inner tensor product (ITP) algebra, allows the substructure of Liouville space to be derived. For SU2×L ₆ mapping over the simply-reducible \(\left\{ {I\tilde H_\upsilon } \right\}\) carrier subspaces, the \(D^k \left( {\tilde U} \right) \times \tilde \Gamma ^{\left[ {\tilde \lambda } \right]} \left( \upsilon \right)\) (L ₆) dual irreps, also arise as a consequence of the Liouville space recoupling termsv≡{k ₁?k _n } being distinct labels for \(\left\{ {I\tilde H_\upsilon } \right\}\) which are themselves amenible to combinatorial analysis within the concept of Rota-Cayley algebra. Hence, theL _n -induced symmetry aspects of multiquantum NMR density matrix formalisms and their dual \(\{ |kq\upsilon :[\tilde \lambda ] > > \} \) tensorial bases of spin cluster problems are derived and the nature of the cooperative, aspect between the individual symmetries comprising the duality is demonstrated, i.e. in the context of the operator bases of Liouville space. These practical arguments correlate, well with those based on an augmented boson pattern algebra derived from a Heisenburg algebra for superoperators, ?_±,?₀. An earlier, treatment of conventional Hilbert space SU2×L ₆ dualitycould only be realised in terms of standard SU2 boson algebra. Since the recoupling Rota-‘field’v for Liouville space is an explicit aspect of the dual mapping, a direct demonstration of cooperativity exists.     

Anticommutativity equation in topological quantum mechanics

We consider topological quantum mechanics as an example of topological field theory and show that its special properties lead to numerous interesting relations for topological correlators in this theory. We prove that the generating function ? for these correlators satisfies the anticommutativity equation (D?F)². We show that the commutativity equation [dB, dB]=0 can be considered as a special case of the anticommutativity equation.     

Frequenzabhängige magnetische Suszeptibilitäten und renormierte Spinwellenenergien von GdCl3

GdCl₃ is a ferromagnet with two equivalent sub-lattices in which the dipolar interaction is comparable with the exchange interaction. In the Callen decoupling approximation the time and temperature dependent Green’s functions are derived and the transversal complex susceptibilitiesχ _xx(ω,h ₀) andχ _yx(ω,h ₀) are calculated. The energies of the acoustical and the optical spinwave modes following from the Green’s functions are renormalized by the magnetization and the spin correlation. The spinwave spectrum, showing an unusual angular dependence, is calculated analytically in the whole Brillouin zone and numerically in the long wavelength region.     

New physics from custodial SU(2) symmetricW interactions at supercolliders

We discuss the observability at LHC or SSC of anomalous 3-boson and 4-boson couplings generated by the SU(2)c preserving operatorO _w . We compute the invariant mass distribution of vector boson pair production viaq \(\bar q\) annihilation and via boson-boson fusion, for all possible channels. both these mechanisms are found to give comparable contributions for SSC and LHC, irrespective of whetherO _w exists or not. We find that the channelsWZ andWγ are particularly suitable for studying whetherO _w really appears in nature, and conclude that an upper limit on the strength of such an interaction which is better than |λ _W |<0.01, should be achievable. This will make a considerable improvement as compared to the indirect limits presently available from LEP1 (|λ _W |<0(1)), and expected from LEP2 (|λ _W |<0(0.1)).     

Spin-spin interaction of Dy3+ ions in KY(WO4)2

The spin-spin interaction of Dy³⁺ ions in a KY(WO₄)₂ single crystal is investigated by electron paramagnetic resonance (EPR) spectroscopy at a temperature of 4.2 K and a frequency of 9.2 GHz. The EPR spectra of ion pairs located in different coordination shells are analyzed. It is revealed that the considerable contribution to the spin-spin interaction of the nearest neighbor ion pair nn is made not only by the magnetic dipole-dipole interaction but also by the isotropic exchange interaction with the parameter I _nn = (+601 ± 17) × 10^?4cm^?1. The exchange interaction in pairs of more widely spaced ions is substantially weaker: I _5n = (?38 ± 3) × 10^?4cm^?1 and I _9n = (+18 ± 4) × 10^?4cm^?1. For the other ion pairs, the magnetic dipole-dipole interaction dominates. It is found that the EPR spectra of single ions and ion pairs exhibit a superhyperfine structure associated with tungsten nuclei.     

\hat sl(2) \oplus \hat sl(2)/\hat sl(2) coset theory is a Hamiltonian reduction of the \hat D(2|1;\alpha ) superalgebra

It is shown that $\hat sl(2)_{k_1 } \oplus \hat sl(2)_{k_2 } /\hat sl(2)_{k_1 + k_2 } $ coset theory is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra $\hat D(2|1;\alpha )$ . In addition, the W algebra of this theory is the commutant of the U _q D(2|1;a) quantum group.     

Antisymmetrization of a mean field calculation of the T-matrix

The usual definition of the prior (post) interactionV(V′) between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projectorA must be included in the definition of the transition operator, T≡V′A + V′A GV. We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate ofT. The theory is illustrated by a calculation of forwardα-α scattering, making use of self consistent symmetries.     

A Mermin–Wagner Theorem for Gibbs States on Lorentzian Triangulations

We establish a Mermin–Wagner type theorem for Gibbs states on infinite random Lorentzian triangulations (LT) arising in models of quantum gravity. Such a triangulation is naturally related to the distribution P of a critical Galton–Watson tree, conditional upon non-extinction. At the vertices of the triangles we place classical spins taking values in a torus M of dimension d, with a given group action of a torus G of dimension d′≤d. In the main body of the paper we assume that the spins interact via a two-body nearest-neighbor potential U(x,y) invariant under the action of G. We analyze quenched Gibbs measures generated by U and prove that, for P-almost all Lorentzian triangulations, every such Gibbs measure is G-invariant, which means the absence of spontaneous continuous symmetry-breaking.     

A remark on the definition of superselection rules in terms of unbounded operators

The mathematical definition of superselection rules in the case when observables are described by unbounded operators in a fixed Hilbert space (for instance, in the frame of Wightman's axioms) is examined. The additional condition \(P_{H_q } D \subset D\) (whereD is the common domain of definition of the operators,H _q is theqth sector, and \(P_{H_q } \) is the projection onH _q ) is found to be sufficient in order to preserve-as in the case of bounded observables—the one-to-one correspondence between reducing subspacesH _q and projections \(P_{H_q } \) from the commutantA′ of the algebraA of observables. This additional condition is equivalent to the physical requirement that every physical vector state can be uniquely represented as a linear combination of physical states, each belonging to some sector.     

A new ℋ -space formalism

The equations governing geometrical objects in ? space are written in terms of operators adapted to families of left shear-freeσ ⁰= 0) cross sections of complexified null infinity (C I ⁺). The concept of ?-conformai weight (HCW) is introduced, and a derivative operatorI _a ^′ , which is closely connected with the covariant derivative but which (unlike the covariant derivative) maps objects having well-defined HCW to other such objects, is defined. A function ?, derived from the Gaussian curvature of left shear-free slicings ofC I ⁺ and having a well-defined HCW, is shown to contain all the curvature information for ? space.     

Support properties of the free measure for Boson fields

Let μ be the measure onI′ (? ^d ) corresponding to the Gaussian process with mean zero and covariance (f,(?Δ+1)^?1 g) onI (? ^d ). It is proven that the set $$( - \Delta _{d - 1} + 1)^{d/4 - \tfrac{1}{2} + \alpha } (1 + x^2 )^{d/4} [\log (2 + x^2 )]^\beta L^2 (\mathbb{R}^d )$$ has μ measure one if α>0 and β>1/2 and μ measure zero if α>0 and β<1/2; here Δ _d?1 is the Laplacian in anyd?1 dimensions whend>1 and Δ₀=Δ.     

BFKL Pomeron in the reaction γ ⊥ * (Q 2)p→ρ ⊥ 0 p at large Q 2 and W

The reaction γ _⊥ ^* (Q ²)p→ρ _⊥ ⁰ p has been studied at large Q ² and W ²/Q ² and low momentum transfers to the nucleon, k _⊥ ² —that is, in the region where the Pomeron exchange mechanism is operative. At sufficiently large Q ², the Pomeron interacts with quarks occurring at small distances, whereby the hard component of the Pomeron is separated, so that the process is governed by the Pomeron of perturbative QCD (BFKL Pomeron). Our calculations indicate that, in vector-meson electroproduction at low k _⊥ ² , the perturbative regime cannot set in fast because, for Q ²≤100 GeV² and, accordingly, for W ²/Q ²≤10⁷, comparatively large distances of $\rho _{q\bar q} > 0.2$ fm are important.     

Invariant states and conditional expectations of the anticommutation relations

The groupG of unitary elements of a maximal abelian von Neumann algebra on a separable, complex Hilbert spaceH acts as a group of automorphisms on the CAR algebraA(H) overH. It is shown that the set ofG-invariant states is a simplex, isomorphic to the set of regular probability measures on aw*-compact setS ofG-invariant generalized free states. The GNS Hilbert space induced by an arbitraryG-invariant state onA(H) supports a *-representation ofC(S); the canonical map ofA(H) intoC(S) can then be locally implemented by a normal,G-invariant conditional expectation.     

Feynman's path integral

Feynman's integral is defined with respect to a pseudomeasure on the space of paths: for instance, letC be the space of pathsq:T?? → configuration space of the system, letC be the topological dual ofC; then Feynman's integral for a particle of massm in a potentialV can be written where $$S_{\operatorname{int} } (q) = \mathop \smallint \limits_T V(q(t)) dt$$ and wheredw is a pseudomeasure whose Fourier transform is defined by for μ∈C′. Pseudomeasures are discussed; several integrals with respect to pseudomeasures are computed.