UV and IR behaviour in QFT and LCQFT with fields as Operator Valued Distributions:Epstein and Glaser revisited

Following Epstein-Glaser's work we show how a QFT formulation based on operator valued distributions (OPVD) with adequate test functions treats original singularities of propagators on the diagonal in a mathematically rigourous way.Thereby UV and/or IR divergences are avoided at any stage, only a finite renormalization finally occurs at a point related to the arbitrary scale present in the test functions.Some well known UV cases are examplified.The power of the IR treatment is shown for the free massive scalar field theory developed in the (conventionally hopeless) mass perturbation expansion.It is argued that the approach should prove most useful for non pertubative methods where the usual determination of counterterms is elusiveComment: 6 pages 2 columns per pag

Higgs mechanism in a light front formulation

We give a simple derivation of the Higgs mechanism in an abelian light front field theory. It is based on a finite volume quantization with antiperiodic scalar fields and a periodic gauge field. An infinite set of degenerate vacua in the form of coherent states of the scalar field that minimize the light front energy, is constructed. The corresponding effective Hamiltonian descibes a massive vector field whose third component is generated by the would-be Goldstone boson. This mechanism, understood here quantum mechanically in the form analogous to the space-like quantization, is derived without gauge fixing as well as in the unitary and the light cone gauge.Comment: 9 page

Critical properties of Φ1+14\Phi^4_{1+1}-theory in Light-Cone Quantization

The dynamics of the phase transition of the continuum $\Phi ^{4}_{1+1}$-theory in Light Cone Quantization is reexamined taking into account fluctuations of the order parameter $$ in the form of dynamical zero mode operators (DZMO) which appear in a natural way via the Haag expansion of the field $\Phi (x)$ of the interacting theory. The inclusion of the DZM-sector changes significantly the value of the critical coupling, bringing it in agreement within 2% with the most recent Monte-Carlo and high temperature/strong coupling estimates. The critical slowing down of the DZMO governs the low momentum behavior of the dispersion relation through invariance of this DZMO under conformal transformations preserving the local light cone structure. The critical exponent $\eta$ characterising the scaling behaviour at $k^2 \to 0$ comes out in agreement with the known value 0.25 of the Ising universality class. $\eta$ is made of two contributions: one, analytic $(75$) and another (25%) which can be evaluated only numerically with an estimated error of 3%. The $\beta$-function is then found from the non-perturbative expression of the physical mass. It is non-analytic in the coupling constant with a critical exponent $\omega=2$. However, at D=2, $\omega$ is not parametrisation independent with respect to the space of coupling constants due to this strong non-analytic behaviour.Comment: Latex, 22 pages, 8 Postscript figures,Appendi

Guidelines for diagnosis and management of the cobalamin-related remethylation disorders cblC, cblD, cblE, cblF, cblG, cblJ and MTHFR deficiency

BACKGROUND: Remethylation defects are rare inherited disorders in which impaired remethylation of homocysteine to methionine leads to accumulation of homocysteine and perturbation of numerous methylation reactions. OBJECTIVE: To summarise clinical and biochemical characteristics of these severe disorders and to provide guidelines on diagnosis and management. DATA SOURCES: Review, evaluation and discussion of the medical literature (Medline, Cochrane databases) by a panel of experts on these rare diseases following the GRADE approach. KEY RECOMMENDATIONS: We strongly recommend measuring plasma total homocysteine in any patient presenting with the combination of neurological and/or visual and/or haematological symptoms, subacute spinal cord degeneration, atypical haemolytic uraemic syndrome or unexplained vascular thrombosis. We strongly recommend to initiate treatment with parenteral hydroxocobalamin without delay in any suspected remethylation disorder; it significantly improves survival and incidence of severe complications. We strongly recommend betaine treatment in individuals with MTHFR deficiency; it improves the outcome and prevents disease when given early

Light-front and conformal field theories in two dimensions

Light-front (LF) quantization of massless fields in two spacetime dimensions is a long-standing and much debated problem. Even though the classical wave-equation is well-documented for almost two centuries, either as problems with initial values in spacetime variables or with initial data on characteristics in light-cone variables, the way to a consistent quantization in both types of frames is still a puzzle in many respects. This is in contrast to the most successful Conformal Field Theoretic (CFT) approach in terms of complex variables z, (z) over bar pioneered by Belavin, Polyakov and Zamolodchikov in the '80s. It is shown here that the 2D-massless canonical quantization in both reference frames is completely consistent provided that quantum fields are treated as Operator-Valued Distributions (OPVD) with Partition of Unity (PU) test functions. We recall first that classical fields have to be considered as distributions (e.g. generalized functions in the Russian literature). Then, a necessary condition on the PU test function follows from the required matching of the classical solutions of the massless differential equations in both types of reference frame. Next we use a mathematical formulation for OPVD, developed in the recent past. Specifically, smooth C-infinity fields are introduced through the convolution operation in the distributional context. Due to the specific behavior of the Fourier-transform of the initial test function, this convolution transform has a well-defined integral in the dual space, whatever the initial choice of the reference frame. The relation to the conformal fields method follows immediately from the transition to Euclidean time and leads directly to explicit calculations of a few correlation functions of the scalar field and its energy-momentum tensor. The LF derivation of the Virasoro algebra is then obtained from the z and (z) over bar expansions of the canonical fields as distributional Laplace-transform in these variables. Finally, the popular and problematic Discretized Light Cone Quantization (DLCQ) method is scrutinized with respect to its zero mode and ultraviolet content as encompassed in the continuum OPVD formulation

Nuclear Mean Field with Correlations at Finite Temperature

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Microscopic Calculation of the Nuclear Mean Field

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