Functional renormalization group approach to neutron matter

The chiral nucleon-meson model, previously applied to systems with equal number of neutrons and protons, is extended to asymmetric nuclear matter. Fluctuations are included in the framework of the functional renormalization group. The equation of state for pure neutron matter is studied and compared to recent advanced many-body calculations. The chiral condensate in neutron matter is computed as a function of baryon density. It is found that, once fluctuations are incorporated, the chiral restoration transition for pure neutron matter is shifted to high densities, much beyond three times the density of normal nuclear matter.Comment: 5 pages, 4 figures, to appear in Phys. Lett.

Die „Gleichzeitigkeit des Ungleichzeitigen“ als Problem transkultureller historischer Komparatistik am Beispiel frühmittelalterlicher Herrschaftslegitimation

At nearly the same time the ruling dynasties changed both in the Frankish realm and in the Islamic caliphate around the middle of the 8th century. A detailed analysis of the religious and cultural conditions shows that rulers had to take into account the respective stages of institutionalization and canonization processes. A close comparative look at the political options open to historical contemporaries in different “cultures” or “civilizations” can make a substantial contribution towards conceptualizing transcultural historiography in global perspective

Die islamische Welt und das christliche Europa zur Zeit Heinrichs V.:Machtverschiebungen und institutionelle Neuansätze

Während der Herrschaftszeit Heinrichs V. wurden die Voraussetzungen für die Neujustierung der christlich-islamischen Mächtekonstellation geschaffen. Hierzu gehört die Entstehung des neuartigen Instituts der geistlichen Ritterorden, die einerseits für das militärische Überleben der Kreuzfahrerherrschaften von entscheidender Bedeutung war, andererseits aber eine neue Form christlichen Ordenslebens begründete, deren Einfluss auf die sich herausbildende ritterliche Kultur kaum zu überschätzen ist. Die Kreuzzüge wirkten als ein wesentlicher Stimulus für das ritterliche Ethos: Ab dem hohen Mittelalter waren Angehörige des niederen wie des hohen Adels, einschließlich der europäischen Monarchen, Angehörige einer kämpfenden militia Christi. Mit dieser Eingliederung der Herrscher in eine zumindest partiell egalitäre Adelsgesellschaft war eine Relativierung des exklusiven Gottesgnadentums der Könige und Kaiser verbunden, was wiederum auf die Neubestimmung des Verhältnisses von regnum und sacerdotium verweist, die sich während der Herrschaft der Salier vollzog. Dieser Entwicklung stand die zeitgleiche Entstehung der Bewegung der Almohaden gegenüber, die zu einer religiösen Neubesinnung auf islamischer Seite führte, die in der Levante mit Nur ad-Din und den Ayyubiden verbunden war. Die Kreuzzüge und die damit verbundene ritterliche Kultur waren wesentliche Elemente der europäischen politischen Kultur des späteren Mittelalters.The institutional foundations for a readjustment of the relationship between Islamic and Christian powers were laid during the reign of Emperor Henry V. With the emergence of the Christian military orders, a completely new form of monastic life came into being. They were indispensable for the military survival of the crusader states; on the other hand, this new form of religious life had momentous consequences for the emergence of chivalry. The crusades provided a powerful stimulus for the development of a chivalric ethos: From the high Middle Ages onwards, members both of the lower and of the higher nobility, including ruling monarchs, saw themselves as belonging to a fighting community, a militia Christi. The absorption of rulers into a partly egalitarian aristocratic culture tended to diminish the divine right of kings and emperors, which was linked to the changing interrelationship of regnum and sacerdotium during the reign of the Salian dynasty. On the Islamic side, this change was matched by a religious revival associated with the movement of the Almohads, and later by Nur ad-Din and the Ayyubids. Crusades and chivalric culture, which were stimulated decisively by developments taking place in this period, turned out to be characteristic elements of European political culture during the later medieval period

Der Dortmunder Totenbund Heinrichs II. und die Reform der futuwwa durch den Bagdader Kalifen al-Nāṣir:Überlegungen zu einer vergleichenden Geschichte mittelalterlicher Institutionen

In the middle ages, political rulers began to use religious institutions in new ways to legitimize their rule. The German king Henry II was the first to establish a new kind of confraternity, of which he became a member himself, together with his wife, the Saxon duke and several bishops. The participants incurred mutual obligations, both liturgical and charitable. The earliest comparable Islamic parallel is the reform of the futuwwa by the caliph al-Nasir. Also in this case, the ruler became a member of a particular religious organization, distinct from the umma at large. However, futuwwa brotherhoods had existed before, but only after the breakdown of Seljuk power had the caliph been in a position to make himself a master of such organizations, using them to promote his religious standing in the wider Sunni world. The relative chances of stability of the institutions depended on many factors, such as ideas concerning the role of monarchs within the respective religious communities, as well as regarding their relationship with political elites. A careful contextualized comparison shows that in western Christianity reciprocal relations of monarchs and other believers were more in line with religious tradition than in Sunni Islam, where it was far more difficult to present the ruler as a member of particular religious confraternities. It becomes evident that the history of political institutions cannot be written without putting them into the wider religious and social context

Herrschergedenken bei den Karolingern und Abbasiden

Unterschiedliche Praktiken des Herrschergedenkens bei christlichen und islamischen Herrschern gehen auf den jeweiligen Entwicklungsstand der „transzendentalen Logik“ zurück, d. h. auf die jeweiligen Annahmen über Möglichkeiten, transzendente Phänomene durch religiöse Praktiken zu beeinflussen. Zu berücksichtigen ist auch der unterschiedliche Ausprägungsgrad von Institutionen: Im Frankenreich existierten in spätantiker Tradition Klöster, die als Grablegen genutzt werden konnten. In frühislamischer Zeit gab es vergleichbare Institutionen nicht; erst später bildeten sich mit den Madrasas Institutionen heraus, die von einer Gemeinschaft getragen wurden und somit die Aufsicht über dort erfolgte Bestattungen übernehmen konnten. Erst die Grabmadrasa schuf die Voraussetzung für kontinuierliches Herrschergedenken, das sich als „soziale Institution“ bezeichnen lässt. Es zeigt sich, dass Formen der Erinnerung an Verstorbene keineswegs anthropologische Konstanten sind, sondern dass jeweils der kulturelle und religiöse Kontext zu berücksichtigen ist. Im Islam entwickelten sich solche Praktiken erst spät, mutmaßlich unter der Einwirkung außerislamischer Vorstellungen, die allerdings, wie in der klassischen islamischen Kultur üblich, unter der Hand islamisiert wurden. Der Blick auf kulturelle Unterschiede kann dabei helfen, die Verabsolutierung von Praktiken der jeweils eigenen Kultur zu vermeiden und zu einer differenzierteren Sicht der historischen Entwicklung zu gelangen.Different practices of commemorating Christian and Islamic rulers are due to different stages of development of the respective „transcendental logic“, i.e. assumptions regarding the possibility to influence transcendental phenomena by religious performance. It is also important to note the different degree of institutionalization: In the Frankish world, there were – as in late antiquity – monasteries that could be used for royal burials. In early Islam there were no comparable institutions. It was only later that the institution of madrasas developed, which were sustained by communities that could also care for burials. The institutionalized madrasa provided the precondition for ongoing practices of commemorating dead rulers. The comparison shows that practices commemorating the dead should not be taken for granted; their development depended on the respective cultural and religious context. In Islam, such practices emerged only at a later stage, possibly influenced by non-Islamic customs, which were tacitly islamicized, as was usual in classical Islamic culture. Pinpointing cultural differences can help to avoid generalizing developments in one’s own culture, clarifying the reasons of different developments

Imperiale Herrschaft an der Peripherie?:Hegemonialstreben und politische Konkurrenz zwischen christlichen und islamischen Herrschern im früh- und hochmittelalterlichen ‛Westen’

The only imperial coronation in medieval Spain, which took place in León in 1135, provides the basis for a comparative analysis of political languages in Christian and Islamic Spain, putting various imperial claims into the context of the political culture of the wider Mediterranean world. The changing use of both Christian and Muslim imperial titles reflects claims to regional hegemony at the periphery of the large oriental power blocks which existed in the Mediterranean until the 12th century. Christian and Muslim monarchs in Spain were not only reacting to rival rulers of the same religion when they adopted or usurped imperial titles, they were also looking at rulers of the other monotheistic religion. The imperial coronation of 1135 took place immediately after the renewed establishment of a second Muslim caliphate in the Muslim West by the Almohads, which, in return, can be understood as the expression of the Almohads’ fight for supremacy in Western Islam against the Almoravids. The latter, in turn, had derived their imperial claims from the caliph in Baghdad, while also rejecting imperial claims to overlordship by the Castilian king, who called himself “emperor of both religions”. Between the 10th and 12th centuries, the changing use of imperial titles by Christian and Muslim rulers was the expression of a competitive principle in which the entanglement of Christian and Islamic Spain became manifest

Thermodynamic phases and mesonic fluctuations in a chiral nucleon-meson model

Studies of the QCD phase diagram must properly include nucleonic degrees of freedom and their thermodynamics in the range of baryon chemical potentials characteristic of nuclear matter. A useful framework for incorporating relevant nuclear physics constraints in this context is a chiral nucleon-meson effective Lagrangian. In the present paper, such a chiral nucleon-meson model is extended with systematic inclusion of mesonic fluctuations using the functional renormalization group approach. The resulting description of the nuclear liquid-gas phase transition shows a remarkable agreement with three-loop calculations based on in-medium chiral effective field theory. No signs of a chiral first-order phase transition and its critical endpoint are found in the region of applicability of the model, at least up to twice the density of normal nuclear matter and at temperatures T<100 MeV. Fluctuations close to the critical point of the first-order liquid-gas transition are also examined with a detailed study of the chiral susceptibility.Comment: 10 pages, 11 figures; references added, discussions enlarge

From asymmetric nuclear matter to neutron stars: a functional renormalization group study

A previous study of nuclear matter in a chiral nucleon-meson model is extended to isospin-asymmetric matter. Fluctuations beyond mean-field approximation are treated in the framework of the functional renormalization group. The nuclear liquid-gas phase transition is investigated in detail as a function of the proton fraction in asymmetric matter. The equations of state at zero temperature of both symmetric nuclear matter and pure neutron matter are found to be in good agreement with realistic many-body computations. We also study the density dependence of the pion mass in the medium. The question of chiral symmetry restoration in neutron matter is addressed; we find a stabilization of the phase with spontaneously broken chiral symmetry once fluctuations are included. Finally, neutron star matter including beta equilibrium is discussed. The model satisfies the constraints imposed by the existence of two-solar-mass neutron stars.Comment: 12 pages, 11 figures, to appear in Phys. Rev. C, references added, figure 5 adde