Single-Particle Green Functions in Exactly Solvable Models of Bose and Fermi Liquids

Based on a class of exactly solvable models of interacting bose and fermi liquids, we compute the single-particle propagators of these systems exactly for all wavelengths and energies and in any number of spatial dimensions. The field operators are expressed in terms of bose fields that correspond to displacements of the condensate in the bose case and displacements of the fermi sea in the fermi case. Unlike some of the previous attempts, the present attempt reduces the answer for the spectral function in any dimension in both fermi and bose systems to quadratures. It is shown that when only the lowest order sea-displacement terms are included, the random phase approximation in its many guises is recovered in the fermi case, and Bogoliubov's theory in the bose case. The momentum distribution is evaluated using two different approaches, exact diagonalisation and the equation of motion approach. The novelty being of course, the exact computation of single-particle properties including short wavelength behaviour.Comment: Latest version to be published in Phys. Rev. B. enlarged to around 40 page

U(1) Gauge Theory as Quantum Hydrodynamics

It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The path integral approach is used to compute the partition function. When gauge fields are included, the constraint brought about by gauge invariance simply means an appropriate linear combination of the gradients of the phase variable and the gauge field is invariant. No gauge fixing is needed in this approach that is closest to the spirit of the gauge principle. We derive an exact formula for the condensate fraction and in case it is zero, an exact formula for the anomalous exponent. We also derive a formula for the vortex strength which involves computing radiation corrections.Comment: 15 pages, Plain LaTeX, final published versio

Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation

We propose a theory which deals with the structure and interactions of volume elements in liquid helium II. The approach consists of two nested models linked via parametric space. The short-wavelength part describes the interior structure of the fluid element using a non-perturbative approach based on the logarithmic wave equation; it suggests the Gaussian-like behaviour of the element's interior density and interparticle interaction potential. The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions. Our approach leads to a unified description of the phonon, maxon and roton excitations, and has noteworthy agreement with experiment: with one essential parameter to fit we reproduce at high accuracy not only the roton minimum but also the neighboring local maximum as well as the sound velocity and structure factor.Comment: 9 pages, 6 figure

Hemokinin-1 Gene Expression Is Upregulated in Microglia Activated by Lipopolysaccharide through NF-κB and p38 MAPK Signaling Pathways

The mammalian tachykinins, substance P (SP) and hemokinin-1 (HK-1), are widely distributed throughout the nervous system and/or peripheral organs, and function as neurotransmitters or chemical modulators by activating their cognate receptor NK1. The TAC1 gene encoding SP is highly expressed in the nervous system, while the TAC4 gene encoding HK-1 is uniformly expressed throughout the body, including a variety of peripheral immune cells. Since TAC4 mRNA is also expressed in microglia, the resident immune cells in the central nervous system, HK-1 may be involved in the inflammatory processes mediated by these cells. In the present study, we found that TAC4, rather than TAC1, was the predominant tachykinin gene expressed in primary cultured microglia. TAC4 mRNA expression was upregulated in the microglia upon their activation by lipopolysaccharide, a well-characterized Toll-like receptor 4 agonist, while TAC1 mRNA expression was downregulated. Furthermore, both nuclear factor-κB and p38 mitogen-activated protein kinase intracellular signaling pathways were required for the upregulation of TAC4 mRNA expression, but not for the downregulation of TAC1 mRNA expression. These findings suggest that HK-1, rather than SP, plays dominant roles in the pathological conditions associated with microglial activation, such as neurodegenerative and neuroinflammatory disorders