Relativistic Particle in Complex Space Time

A modified version of the bilocal particle is presented in terms of complex space time. Unusual constraint structure of the model is studied, and a new concept of the physical equivalence is proposed in accordance with Dirac's conjecture. It is found that in the quantum theory the physical state conditions are compatible with existence of eigenstates of momentum only when the dimension of space time is four. An example of scattering amplitude is calculated.Comment: 15 page

BRS Cohomology of a Bilocal Model

We present a model in which a gauge symmetry of a field theory is intrinsic in the geometry of an extended space time itself. A consequence is that the dimension of our space time is restricted through the BRS cohomology. If the Hilbert space is a dense subspace of the space of all square integrable $C^{\infty}$ functions, the BRS cohomology classes are nontrivial only when the dimension is two or four.Comment: 15 pages, LaTeX. The original title, ``On the Dimension of the Space time'', is change

Moyal Quantization for Constrained System

We study the Moyal quantization for the constrained system. One of the purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in terms of the Weyl symbols becomes different from the classical Hamiltonian for the constrained system, which is related to the fact that the naively constructed WW correspondence is not one-to-one any more. In the Moyal quantization a geometrical meaning of the constraints is clear. In our proposal, the 2nd class constraints are incorporated into the definition of the WW correspondence by limiting the phasespace to the hypersurface. Even though we assume the canonical commutation relations in the formulation, the Moyal brackets between the Weyl symbols yield the same results as those for the constrained system derived by using the Dirac bracket formulation.Comment: 25 page

A Bilocal Field Theory in Four Dimensions

A bilocal field theory having M\"{o}bius gauge invariance is proposed. In four dimensions there exists a zero momentum state of the first quantized model, which belongs to a non-trivial BRS cohomology class. A field theory lagrangian having a gauge invariance only in four dimensions is constructed.Comment: 13 pages, TEP-9R, LaTe

Role of prostaglandin E receptor subtypes EP2 and EP4 in autocrine and paracrine functions of vascular endothelial growth factor in the inner ear

<p>Abstract</p> <p>Background</p> <p>The physiological effects of prostaglandin E1 (PGE1) and prostaglandin E2 (PGE2) are mediated by the prostaglandin E receptor subtypes EP1, EP2, EP3, and EP4, and the respective agonists have been purified. PGE1 and PGE2 can increase the production of vascular endothelial growth factor (VEGF), particularly through EP2 and EP4. The biological effects of VEGF are mediated by the phosphotyrosine kinase receptors fms-related tyrosine kinase-1 (Flt-1) and fetal liver kinase-1 (Flk-1). Here we examined the effects of EP2 and EP4 agonists on the production of VEGF proteins and <it>VEGF </it>messenger RNAs (mRNAs) in the inner ear, using an enzyme-linked immunosorbent assay and the real-time quantitative reverse transcription-polymerase chain reaction, respectively. We also examined the localization of EP2, VEGF, Flt-1, and Flk-1 in the cochlea by immunohistochemistry.</p> <p>Results</p> <p>The expression of EP2 occurred in the cochlea, and the local application of an EP2 or EP4 agonist increased VEGF protein and <it>VEGF </it>mRNA levels in the inner ear. Furthermore, the intensity of the VEGF immunoreactivity in the spiral ganglion appeared to be increased by the local EP2 or EP4 agonist treatment. Immunoreactivity for Flt-1, and Flk-1 was found in the cochlear sensory epithelium, spiral ganglion, spiral ligament, and stria vascularis.</p> <p>Conclusions</p> <p>These findings demonstrate that EP2 and EP4 agonists stimulate VEGF production in the inner ear, particularly in the spiral ganglions. Moreover, the Flt-1 and Flk-1 expression observed in the present study suggests that VEGF has autocrine and paracrine actions in the cochlea. Thus, EP2 and EP4 might be involved in the mechanisms underlying the therapeutic effects of PGE1 on acute sensorineural hearing loss via VEGF production.</p