We demonstrate coherent anti-Stokes Raman scattering (CARS) heterodyne spectral interferometry for retrieval of the real and imaginary components of the third-order nonlinear susceptibility (chi(3)) of molecular vibrations. Extraction of the imaginary component of chi(3) allows a straightforward reconstruction of the vibrationally resonant signal that is completely free of the electronic nonres...

The electroweak process pp̄ → lνγγ is calculated at tree level, including finite W width effects. In order to obtain a gauge invariant amplitude, the imaginary parts of WWγ triangle graphs and WWγγ box diagrams have to be included, in addition to resumming the imaginary contributions to the W vacuum polarization. We demonstrate the existence of a radiation amplitude zero in pp̄ → Wγγ → lνγγ, and ...

Nonresonant second harmonic generation (SHG) phase and amplitude measurements obtained from the silica-water interface at varying pH values an ionic strength of 0.5 M point to existence a nonlinear susceptibility term, which we call ?X(3), that is associated with 90° shift. Including this contribution in model for total effective second-order produces reasonable estimates interfacial potentials...

We find that single spin asymmetries in NRQCD are non-vanishing in general. They are proportional to the imaginary parts of some nonperturbative matrix elements. With statistics of about 10 identified J/ψ’s, or 10 identified χ2, it is possible to measure these imaginary parts even if they are an order of magnitude smaller than the real parts. Such statistics are quite reasonable at polarised HE...

The similar sublattices of a planar lattice can be classified via its multiplier ring. The latter is the ring of rational integers in the generic case, and an order in an imaginary quadratic field otherwise. Several classes of examples are discussed, with special emphasis on concrete results. In particular, we derive Dirichlet series generating functions for the number of distinct similar subla...

We consider thermal n-point Green functions in the framework of quantum field theory at finite temperature. We show how analytic continuations from imaginary to real energies relate these functions originally defined in the imaginary-time formalism to retarded and advanced real-time ones. The described method is valid to all orders of perturbation theory. It has the further advantage that it is...

The imaginary cone of a Kac-Moody Lie algebra is the convex hull of zero and the positive imaginary roots. This paper studies the imaginary cone for a class of root systems of general Coxeter groups W . It is shown that the imaginary cone of a reflection subgroup of W is contained in that of W , and that for irreducible infinite W of finite rank, the closed imaginary cone is the only non-zero, ...

In a related paper we have obtained that the effective action for a κ-deformed quantum field theory has a real and an imaginary part. The real part is half the sum of the κ-deformed zero mode frequencies, while the imaginary part is proportional to the sum of the squares of the zero mode frequencies, being the proportionality constant equal to the inverse of 2πκ. Here we calculate this imaginar...

This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrödinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the nonrelativistic theory. In analogy to the nonrelativistic case, the ...