Calculation of Reggeon Vertices in QCD

The method of calculation of effective vertices of interaction of the Reggeized gluon and quark with particles in QCD in the next-to-leading order is developed. The method is demonstrated in the case of already known vertices of both gluon-gluon and quark-quark transitions in the scattering of gluons and quarks on the Reggeized gluon. It is used for the calculation of the gluon-quark transition in the scattering on the Reggeized quark.Comment: 27 pages, LaTex, 1 figure, uses axodraw.st

The Quark Impact Factors

We calculate in the next-to-leading approximation the non-forward quark impact factors for both singlet and octet color representation in the $t$-channel. The integral representation of the octet impact factor in the general case of arbitrary space-time dimension and massive quark flavors is used to check the so-called "second bootstrap condition" for the gluon Reggeization at the next-to-leading logarithmic approximation in perturbative QCD. We find that it is satisfied for both helicity conserving and non-conserving parts. The integrations are then performed for the explicit calculation of the impact factors in the massless quark case.Comment: 23 pages, LaTeX, 1 EPS figure, uses epsf.sty and axodraw.st

Electroproduction of two light vector mesons in next-to-leading BFKL: study of systematic effects

The forward electroproduction of two light vector mesons is the first example of a collision process between strongly interacting colorless particles for which the amplitude can be written completely within perturbative QCD in the Regge limit with next-to-leading accuracy. In a previous paper we have given a numerical determination of the amplitude in the case of equal photon virtualities by using a definite representation for the amplitude and a definite optimization method for the perturbative series. Here we estimate the systematic uncertainty of our previous determination, by considering a different representation of the amplitude and different optimization methods of the perturbative series. Moreover, we compare our result for the differential cross section at the minimum momentum transfer with a different approach, based on collinear kernel improvement.Comment: 17 pages, 11 figures; journal version, new figures and discussion adde

The quark part of the non-forward BFKL kernel and the ``bootstrap'' for the gluon Reggeization

We calculate the quark part of the kernel of the generalized non-forward BFKL equation at non-zero momentum transfer $t$ in the next-to-leading logarithmic approximation. Along with the quark contribution to the gluon Regge trajectory, this part includes pieces coming from the quark-antiquark production and from the quark contribution to the radiative corrections in one-gluon production in the Reggeon-Reggeon collisions. The results obtained can be used for an arbitrary representation of the colour group in the $t-$channel. Using the results for the adjoint representation, we demonstrate explicitly the fulfillment of the ``bootstrap'' condition for the gluon Reggeization in the next-to-leading logarithmic approximation in the part concerning the quark contribution.Comment: 26 pages, LaTeX, uses axodraw.sty; revised final comment; to appear on Phys. Rev.

The Gluon Impact Factors

We calculate in the next-to-leading approximation the non-forward gluon impact factors for arbitrary color state in the $t$-channel. In the case of the octet state we check the so-called "second bootstrap condition" for the gluon Reggeization in QCD, using the integral representation for the impact factors. The condition is fulfilled in the general case of an arbitrary space-time dimension and massive quark flavors for both helicity conserving and non-conserving parts.Comment: 32 pages, LaTeX, 1 EPS figure, uses epsf.sty and axodraw.st

Narrative, postmodernity and the problem of "religious illiteracy"

It is popular nowadays to claim not only that narrative is the most effective way to communicate religious knowledge but also that narrative provides the framework within which religious lifestyles and practices are meaningful. However, many today lack familiarity with the narratives of traditional religions. In other words, they suffer from ‘religious illiteracy’. This article considers the problem of how religion can become meaningful to such people. The view that religion can be divested of its outdated cultural accoutrements and presented in a form that resonates with postmodern secular culture is considered and found to be problematic. If acquiring a religion is like acquiring a culture, or a language, it seems unlikely that a deeper appreciation of a religious tradition will be facilitated by divesting it of its traditional cultural expressions. Moreover, the view that religious lifestyles should be emphasised rather than religious belief seems to be more a symptom of the problem of ‘religious illiteracy’ than a solution to it. The article concludes that both of these responses fail to provide a solution to the problem and that an alternative strategy is urgently required

Metaphor, religious language and religious experience

Is it possible to talk about God without either misrepresentation or failing to assert anything of significance? The article begins by reviewing how, in attempting to answer this question, traditional theories of religious language have failed to sidestep both potential pitfalls adequately. After arguing that recently developed theories of metaphor seem better able to shed light on the nature of religious language, it considers the claim that huge areas of our language and, consequently, of our experience are shaped by metaphors. Finally, it considers some of the more significant implications of this claim for our understanding of both religious language and religious experience

The pragmatics of defining religion in a multi-cultural world

Few seem to have difficulty in distinguishing between religious and secular institutions, yet there is widespread disagreement regarding what "religion" actually means. Indeed, some go so far as to question whether there is anything at all distinctive about religions. Hence, formulating a definition of "religion" that can command wide assent has proven to be an extremely difficult task. In this article I consider the most prominent of the many rival definitions that have been proposed, the majority falling within three basic types: intellectual, affective and functional definitions. I conclude that there are pragmatic reasons for favouring the formerly popular view that essentialist definitions of "religions" are inadequate, and that religions should be construed, instead, as possessing a number of "family resemblances". In so arguing, I provide a response to the view that there is nothing distinctive about religions, as well as to the recent claim that religions do not exist

Internal realism, religious pluralism and ontology

Internalist pluralism is an attractive and elegant theory. However, there are two apparently powerful objections to this approach that prevent its widespread adoption. According to the first objection, the resulting analysis of religious belief systems is intrinsically atheistic; while according to the second objection, the analysis is unsatisfactory because it allows religious objects simply to be defined into existence. In this article, I demonstrate that an adherent of internalist pluralism can deflect both of these objections, and in the course of so arguing, I deploy a distinction between “conceptual-scheme targetability” and “successful conceptual-scheme targeting”

A solution of a problem of Sophus Lie: Normal forms of 2-dim metrics admitting two projective vector fields

We give a complete list of normal forms for the 2-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This solves a problem posed by Sophus Lie.Comment: This is an extended version of the paper that will appear in Math. Annalen. Some typos were corrected, references were updated, title was changed (as in the journal version). 31 page