A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories

We propose an alternative axiomatic description for non-commutative field theories (NCFT) based on some ideas by Soloviev to nonlocal quantum fields. The local commutativity axiom is replaced by the weaker condition that the fields commute at sufficiently large spatial separations, called asymptotic commutativity, formulated in terms of the theory of analytic functionals. The question of a possible violation of the CPT and Spin-Statistics theorems caused by nonlocality of the commutation relations $[\hat{x}_\mu,\hat{x}_\nu]=i\theta_{\mu\nu}$ is investigated. In spite of this inherent nonlocality, we show that the modification aforementioned is sufficient to ensure the validity of these theorems for NCFT. We restrict ourselves to the simplest model of a scalar field in the case of only space-space non-commutativity.Comment: The title is new, and the analysis in the manuscript has been made more precise. This revised version is to be published in J.Math.Phy

Supersymmetric Distributions, Hilbert Spaces of Supersymmetric Functions and Quantum Fields

The recently investigated Hilbert-Krein and other positivity structures of the superspace are considered in the framework of superdistributions. These tools are applied to problems raised by the rigorous supersymmetric quantum field theory.Comment: 24 page

Implication functions in interval-valued fuzzy set theory

Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory

Fatal attraction: a critique of Carl Schmitt's international political and legal theory

The ongoing Schmitt revival has extended Carl Schmitt's reach over the fields of international legal and political theory. Neo-Schmittians suggest that his international thought provides a new reading of the history of international law and order, which validates the explanatory power of his theoretical premises – the concept of the political, political decisionism, and concrete-order-thinking. Against this background, this article mounts a systematic reappraisal of Schmitt's international thought in a historical perspective. The argument is that his work requires re-contextualization as the intellectual product of an ultra-intense moment in Schmitt's friend/enemy distinction. It inscribed Hitler's ‘spatial revolution’ into a full-scale reinterpretation of Europe's geopolitical history, grounded in land appropriations, which legitimized Nazi Germany's wars of conquest. Consequently, Schmitt's elevation of the early modern nomos as the model for civilized warfare – the ‘golden age’ of international law – against which American legal universalism can be portrayed as degenerated, is conceptually and empirically flawed. Schmitt devised a politically motivated set of theoretical premises to provide a historical counter-narrative against liberal normativism, which generated defective history. The reconstruction of this history reveals the explanatory limits of his theoretical vocabulary – friend/enemy binary, sovereignty-as-exception, nomos/universalism – for past and present analytical purposes. Schmitt's defective analytics and problematic history compromise the standing of his work for purposes of international theory

Intertemporal evaluation criteria for climate change policy: the basic ethical issues

The evaluation of long-term effects of climate change in cost-benefit analysis has a long tradition in environmental economics. Since the publication of the Stern Review in 2006 the debate about the 'appropriate' discounting of future welfare and utility levels was revived and the most renowned scholars of the profession participated in this debate. But it seems that some contributions dealing with the Stern Review and the Review itself mixed up normative and positive issues to defend the own position. Furthermore, as we argue in this contribution, it also seems that the debate misses the heart of the problem. The aim of this work is to bring together economic and philosophical reasoning about justice and intergenerational equity in the context of climate change. So we adopt the normative view in order to present the most important ethical issues that, particularly in the context of climate policy, are most relevant for the choice of intertemporal welfare criteria. Subsequently we explore whether ethical considerations may also be helpful to determine the parameter values (or at least to delimit their range) which, after the choice of some type of intertemporal social welfare function, are needed to specify the concrete criterion that is employed to make decisions on climate policy. --Intertemporal ethics,Distribution,Discounting,Climate Change

Linking Strategic Interaction and Bargaining Theory. The Harsanyi - Schelling Debate on the Axiom of Symmetry

This paper analyses the early contributions of John Harsanyi and Thomas C. Schelling to bargaining theory. In his work, Harsanyi (1956) draws Nash’s solution to two-person cooperative games from the bargaining model proposed by Zeuthen (1930). Whereas Schelling (1960) proposes a multi-faceted theory of conflict that, without dismissing the assumption of rational behaviour, points out some of its paradoxical consequences. Harsanyi and Schelling’s contrasting views on the axiom of symmetry, as postulated by Nash (1950), are then presented. The analysis of this debate illustrates that, although in the early 1960s two different approaches to link strategic interaction and bargaining theory were proposed, only Harsanyi’s insights were fully developed later. Lastly, the causes of this evolution are assessed.bargaining, game theory, symmetry

Theories of Fairness and Reciprocity

Most economic models are based on the self-interest hypothesis that assumes that all people are exclusively motivated by their material self-interest. In recent years experimental economists have gathered overwhelming evidence that systematically refutes the self-interest hypothesis and suggests that many people are strongly motivated by concerns for fairness and reciprocity. Moreover, several theoretical papers have been written showing that the observed phenomena can be explained in a rigorous and tractable manner. These theories in turn induced a new wave of experimental research offering additional exciting insights into the nature of preferences and into the relative performance of competing theories of fairness. The purpose of this paper is to review these recent developments, to point out open questions, and to suggest avenues for future research

Popular Constitutionalism and the Rule of Recognition: Whose Practices Ground U.S. Law?

The law within each legal system is a function of the practices of some social group. In short, law is a kind of socially grounded norm. H.L.A Hart famously developed this view in his book, The Concept of Law, by arguing that law derives from a social rule, the so-called “rule of recognition.” But the proposition that social facts play a foundational role in producing law is a point of consensus for all modern jurisprudents in the Anglo-American tradition: not just Hart and his followers in the positivist school, most prominently Joseph Raz and Jules Coleman, but also the anti-positivist Ronald Dworkin, who argues that law necessarily synthesizes moral considerations with social facts. But which group’s practices ground each legal system? In particular, which group’s practices undergird U.S. law? Positivists since Hart have universally pointed to either officials or judges as the “recognitional community” (my term): the group such that its rules, conventions, cooperative activities, or practices in some other sense are the social facts from which the law of a given legal system derives. So Hart and all other positivists would identify either U.S. officials or U.S. judges as the recognitional community for U.S. law. This Article grapples with the tension between the positivist’s official- or judge-centered account of the recognitional community and the “popular constitutionalism” now so widely defended by constitutional scholars such as Larry Kramer, Robert Post, Reva Siegel, Mark Tushnet, Jeremy Waldron, and many others. Surely the popular constitutionalist would want to claim that U.S. citizens, not judges or officials, are the recognitional community for U.S. law. I term this position “deep popular constitutionalism.” Indeed, it turns out that Dworkin’s account of law, in its ambition to generate associative moral obligations for the citizenry as a whole, implies deep popular constitutionalism. Here there is a disagreement, hitherto unnoticed, between Dworkin and the positivists. My solution to this disagreement – to the debate between deep popular constitutionalists and deep official or judicial supremacists -- is to dissolve it by providing a group-relative account of law. Social norms, such as norms of dress or eating, are clearly group-relative. A particular dressing or eating behavior may be socially appropriate relative to one group’s norms, yet socially inappropriate relative to another’s. This Article extends the group-relative view from social norms to law itself, with a particular focus on U.S. law and constitutionalism. Part I surveys the jurisprudential literature. It shows how Hart and successor positivists identify the rule of recognition as a social practice engaged in by officials or some subset of officials (judges), rather than citizens generally, and argues that Dworkin by contrast sees the citizenry as a whole as his recognitional community. Parts II and III defend a group-relative account of law. Part II argues, with reference to the U.S. experience, that multiple groups can simultaneously instantiate the kind of social fact that undergirds law, be it a convention, a social norm, a “shared cooperative activity” (SCA), or something else. At many points in U.S. constitutional history, multiple official or citizen groups, defined along departmental, partisan, regional, state-federal, religious, or other lines, have accepted competing rules of recognition for U.S. law. Part III argues that “law” functions, primarily, as either an explanatory or a normative construct, and that insisting on a single recognitional community for each legal system would be arbitrary, both for explanatory purposes and for normative purposes. Part IV considers the many implications of the group-relative account for U.S. constitutional theory – in particular, for popular constitutionalism

Convex ordering and quantification of quantumness

The characterization of physical systems requires a comprehensive understanding of quantum effects. One aspect is a proper quantification of the strength of such quantum phenomena. Here, a general convex ordering of quantum states will be introduced which is based on the algebraic definition of classical states. This definition resolves the ambiguity of the quantumness quantification using topological distance measures. Classical operations on quantum states will be considered to further generalize the ordering prescription. Our technique can be used for a natural and unambiguous quantification of general quantum properties whose classical reference has a convex structure. We apply this method to typical scenarios in quantum optics and quantum information theory to study measures which are based on the fundamental quantum superposition principle.Comment: 9 pages, 2 figures, revised version; published in special issue "150 years of Margarita and Vladimir Man'ko