On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomorphism theorem cannot be generalized to algebras if the Z_n-grading or other structures are added, e.g., a linear form. We work with pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford algebras'. It turns out, that in this sense, all multi-vector Clifford algebras of the same quadratic but different bilinear forms are non-isomorphic. The usefulness of such algebras in quantum field theory and superconductivity was shown elsewhere. Allowing for arbitrary bilinear forms however spoils their diagonalizability which has a considerable effect on the tensor decomposition of the Clifford algebras governed by the periodicity theorems, including the Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1} \otimes Cl_{1,1}. The general case used in quantum field theory lacks this feature. Theories with non-symmetric bilinear forms are however needed in the analysis of multi-particle states in interacting theories. A connection to q-deformed structures through nontrivial vacuum states in quantum theories is outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa, Mexico, June 27 - July 4, 199

A limiting velocity for quarkonium propagation in a strongly coupled plasma via AdS/CFT

We study the dispersion relations of mesons in a particular hot strongly coupled supersymmetric gauge theory plasma. We find that at large momentum k the dispersion relations become omega = v_0 k + a + b/k + ..., where the limiting velocity v_0 is the same for mesons with any quantum numbers and depends only on the ratio of the temperature to the quark mass T/m_q. We compute a and b in terms of the meson quantum numbers and T/m_q. The limiting meson velocity v_0 becomes much smaller than the speed of light at temperatures below but close to T_diss, the temperature above which no meson bound states at rest in the plasma are found. From our result for v_0, we find that the temperature above which no meson bound states with velocity v exist is T_diss(v) \simeq (1-v^2)^(1/4) T_diss, up to few percent corrections.We thus confirm by direct calculation of meson dispersion relations a result inferred indirectly in previous work via analysis of the screening length between a static quark and antiquark in a moving plasma. Although we do not do our calculations in QCD, we argue that the qualitative features of the dispersion relation we compute, including in particular the relation between dissociation temperature and meson velocity, may apply to bottomonium and charmonium mesons propagating in the strongly coupled plasma of QCD. We discuss how our results can contribute to understanding quarkonium physics in heavy ion collisions.Comment: 57 pages, 12 figures; references adde

Perforated acute appendicitis resulting from appendiceal villous adenoma presenting with small bowel obstruction: a case report

<p>Abstract</p> <p>Background</p> <p>A villous adenoma is an extremely rare benign tumour in the appendix, in contrast to other benign appendiceal lesions. The clinical features are usually asymptomatic. Acute appendicitis is the most common complication with the lesion obstructing the orifice of the appendiceal lumen. Thus, a villous adenoma is usually found during surgical intervention for acute appendicitis. Mechanical obstruction induced by acute perforated appendicitis has been previously reported. Acute appendicitis caused by a villous adenoma presenting with acute intestinal obstruction has not been previously reported.</p> <p>Case presentation</p> <p>A 78-year-old woman presented to our Emergency Department with diffuse abdominal pain and tenderness. The abdominal plain film and computed tomography revealed an intestinal obstruction. After surgical intervention, the ruptured appendix was shown to be associated with intestinal obstruction. The post-operative pathologic diagnosis was an appendiceal villous adenoma.</p> <p>Conclusions</p> <p>This is the first report describing an appendiceal villous adenoma, which is an occasional cause of perforated acute appendicitis, presenting as a complete intestinal obstruction. We emphasize that in elderly patients without a surgical history, the occult cause of complete intestinal obstruction must be determined. If an appendiceal tumour is diagnosed, an intra-operative frozen section is suggested prior to selecting a suitable method of surgical intervention.</p