On hyperlogarithms and Feynman integrals with divergences and many scales

It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples of integrations of three- and four-point integrals in Schwinger parameters with non-trivial kinematic dependence, involving setups with off-shell external momenta and differently massive internal propagators. The full set of Feynman graphs admissible to parametric integration is not yet understood and we discuss some counterexamples to the crucial property of linear reducibility. Furthermore we clarify how divergent integrals can be approached in dimensional regularization with this algorithm.Comment: 26 pages, 11 figures, 2 tables, explicit results in ancillary file "results" and on http://www.math.hu-berlin.de/~panzer/ (version as in JHEP; link corrected

Feynman integrals via hyperlogarithms

This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future directions.Comment: 8 pages, 5 figures, Proceedings of "Loops & Legs 2014", Weimar (Germany), April 27 -- May

Graphical functions in parametric space

Graphical functions are positive functions on the punctured complex plane $\mathbb{C}\setminus\{0,1\}$ which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and Nakanishi, which implies the real analyticity of graphical functions. Moreover we prove a formula that relates graphical functions of planar dual graphs.Comment: v2: extended introduction, minor changes in notation and correction of misprint

Feynman integral relations from parametric annihilators

We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of Loeser and Sabbah, we conclude that the number of master integrals is computed by the Euler characteristic of the Lee-Pomeransky polynomial. We illustrate techniques to compute this Euler characteristic in various examples and compare it with numbers of master integrals obtained in previous works.Comment: v2: new section 3.1 added, several misprints corrected and additional remark

Childhood Obesity: The Role of the Mental Health Professional

This work consists of two major components: understanding the nature of childhood obesity and providing clinical services. Factors responsible for the current epidemic will be outlined, as will the current definition of the disorder. Statistical data regarding the epidemiology of weight disorders in childhood will be provided in order to give a perspective of the problem. Various obesity trajectories and their differential diagnostic and treatment issues will be thoroughly explored. The intervention section intends to help clinicians to evaluate salient factors in assessing the obese child and to identify appropriate goals and treatment methods. The course will provide vital information for all mental health professionals involved in the care of overweight or obese children

The neuroendocrinological sequelae of stress during brain development: the impact of child abuse and neglect

Severe stress during the sensitive periods of neurodevelopment, (which include the prenatal period, infancy, childhood and adolescence), has a long-lasting organizing effect on the brain and stress axes. Child abuse and neglect thus exert a cumulative harmful effect on neuroendocrinological development, which persists into adulthood. It is not merely the memory of the trauma which leaves a mark, but rather the effect on neurodevelopment which negatively influences the ability of adult survivors of childhood maltreatment to cope with current stressors. The victims of child abuse and neglect are likely to maltreat their own children and so perpetuate the intergenerational transmission of child maltreatment. In this paper relevant normal brain development is first summarized. Child abuse/neglect is next discussed with detailed reference to the aberrant neuroendocrinological development that is known to occur. We specifically examine effects on the hypothalamo-pituitary-adrenal and central noradrenergic-sympathoadrenomedullary stress axes and other neurotransmitter systems before turning to changes described in the cerebral volumes, corpus callosum and cortical hemispheres, prefrontal cortex and amygdalae, superior temporal gyrus, hippocampus as well as the cerebellar vermis.African Journal of Psychiatry Vol. 11 (1) 2008: pp. 29-3

Feynman integrals and hyperlogarithms

We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in terms of multiple polylogarithms, to all orders in the epsilon-expansion. These integrals can be computed effectively with the presented program. We include interesting examples of explicit results for Feynman integrals with up to 6 loops. In particular we present the first exactly computed counterterm in massless phi^4 theory which is not a multiple zeta value, but a linear combination of multiple polylogarithms at primitive sixth roots of unity (and divided by $\sqrt{3}$). To this end we derive a parity result on the reducibility of the real- and imaginary parts of such numbers into products and terms of lower depth.Comment: PhD thesis, 220 pages, many figure