Continuity properties of factors in polar decompositions of matrices with respect to inde®nite scalar products are studied. The matrix having the polar decomposition and the inde®nite scalar product are allowed to vary. Closely related properties of a self-adjoint (with respect to an inde®nite scalar product) perturbed matrix to have a self-adjoint square root, or to have a representation of th...

We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for noncommutative scalar field theory. Then from the Moyal commutators, we demonstrate that the microscopic causality is satisfied for scalar fields on noncommutative spacetime. We construct the Feynman propagator of Moyal star-product for noncommutative scalar field theory. PACS numbers: 11...

Scalar product protocol aims at securely computing the dot product of two private vectors. As a basic tool, the protocol has been widely used in privacy preserving distributed collaborative computations. In this paper, at the expense of disclosing partial sum of some private data, we propose a linearly efficient even-dimension scalar product protocol (EDSPP) without employing expensive homomorp...

In this work we define a scalar product " weighted " with the scalar factor R and show how to find a normalized wave function for the supersymmetric quantum FRW cosmological model using the idea of supersymmetry breaking selection rules under local n=2 conformal supersymmetry. We also calculate the expectation value of the scalar factor R in this model and its corresponding behaviour.

In the framework of scalar-vector dominance we calculate the hadronic matrix elements of scalar and tensor effective quark currents induced by virtual leptoquark interactions. Combined bounds on the product of couplings and leptoquark masses are obtained from experimental data.

We examine the interpretation of the light scalar meson nonet as bound states of the scalar diquark and the scalar antidiquark using the QCD sum rule approach. Our results are obtained by means of the operator product expansion (OPE) including operators up to dimension 8. They show no evidence of the coupling of the tetraquark states to the light scalar meson nonet. Pacs: 11.55.Hx, 12.38.Aw, 12...

Jack polynomials in superspace, orthogonal with respect to a " combinatorial " scalar product, are constructed. They are shown to coincide with the Jack polynomials in superspace, orthogonal with respect to a " physical " scalar product, introduced in [5] as eigenfunctions of a supersymmetric quantum mechanical many-body problem. The results of this article rely on generalizing (to include an e...

Many enumerative problems can be expressed using the scalar product of symmetric functions. As we shall see, we can set up expressions for the generating functions of objects which possess a certain kind of regularity as a scalar product. Two examples of this are k-regular graphs (graphs in which each vertex is of degree k), and secondly we have a class of semi-standard Young tableaux in which ...

Jack polynomials in superspace, orthogonal with respect to a “combinatorial” scalar product, are constructed. They are shown to coincide with the Jack polynomials in superspace, orthogonal with respect to an “analytical” scalar product, introduced in [5] as eigenfunctions of a supersymmetric quantum mechanical many-body problem. The results of this article rely on generalizing (to include an ex...

We work out finite-dimensional integral formulae for the scalar product of genus one states of the group G Chern-Simons theory with insertions of Wilson lines. Assuming convergence of the integrals, we show that unitarity of the elliptic KnizhnikZamolodchikov-Bernard connection with respect to the scalar product of CS states is closely related to the Bethe Ansatz for the commuting Hamiltonians ...