Quantum field theories with fermions in the Schrödinger representation

This thesis is concerned with the Schrödinger representation of quantum field theory. We describe techniques for solving the Schrödinger equation which supplement the standard techniques of field theory. Our aim is to develop these to the point where they can readily be used to address problems of current interest. To this end, we study realistic models such as gauge theories coupled to dynamical fermions. For maximal generality we consider particles of all physical spins, in various dimensions, and eventually, curved spacetimes. We begin by considering Gaussian fields, and proceed to a detailed study of the Schwinger model, which is, amongst other things, a useful model for (3+1) dimensional gauge theory. One of the most important developments of recent years is a conjecture by Mal-dacena which relates supergravity and string/M-theory on anti-de-Sitter spacetimes to conformal field theories on their boundaries. This correspondence has a natural interpretation in the Schrödinger representation, so we solve the Schrödinger equation for fields of arbitrary spin in anti-de-Sitter spacetimes, and use this to investigate the conjectured correspondence. Our main result is to calculate the Weyl anomalies arising from supergravity fields, which, summed over the supermultiplets of type JIB supergravity compactified on AdS(_s) x S(^5) correctly matches the anomaly calculated in the conjecturally dual N = 4 SU{N) super-Yang-Mills theory. This is one of the few existing pieces of evidence for Maldacena's conjecture beyond leading order in TV

Jesus, Barabbas and the People: The Climax of Luke’s Trial Narrative and Lukan Christology (Luke 23.13-25)

This article argues that the nuance and function given to the Barabbas pericope in Luke’s trial narrative differs significantly from that expressed by the other evangelists. It submits that Luke depicts Jesus’ death to be the result of a substitution between the acquitted Jesus and the insurrectionist and murderer Barabbas. Furthermore, the third evangelist has crafted his trial narrative so as to highlight the representative nature of this death, thereby developing Jesus’ narrative identity as the Messiah. It is concluded that Luke’s crafting of his trial narrative raises questions for the prevalent view that the third evangelist has not integrated the idea of substitution into his understanding of Jesus’ death

Luke's readers - a study of Luke 4.22-8; Acts 13.46; 18.6; 28.28 and Luke 21.5-36

The work is presented as a contribution to the case for understanding Luke/Acts as addressed not primarily to Gentiles but to people who will assess Christianity with norms provided by first-century Judaism. Part 1 sets out to show that there is in Luke/Acts no turning of God's interest away from the Jews and to the Gentiles. A detailed exegesis of Lk 4.33-8 reveals that vv 25-7 are not concerned to make this point (chapter 1). Luke works with a pattern of God's twin concern that both Jews and Gentiles should be reached with the gospel. Acts 13.46; 18.6 and 28.28 do not overturn this pattern: Acts 28.28 exhibits the pattern; Acts 13.46 is based on a commitment to the priority of the Jews which for Luke remains in force; all three verses take their place as part of complex apologetic designed to keep the widespread Jewish unbelief from being used as a means of discrediting Christianity (chapter 2). Part 2 offers a case for understanding Lk 21 as Luke's refutation of a Jewish use of the saying about the destruction and renewal of the Temple as a polemic castigating Christianity as insurrectionist and violently opposed to main-stream Judaism. In significant contrast to Mk 13, the content of Lk 21, and its context, make for a Lukan Jesus who, though he had to announce the destruction of the Temple (as did Jeremiah held it in highest honour. Editorial deletions and the form of Acts 6.14 encourage the reader to connect the accusation there with Lk 21 (chapter 3). There is evidence for a Jewish polemical use of the Temple saying in the form which mentions bother destructions an renewal. The sense of the polemic is best understood against the background of Qumran thought: Christians are fomenting a violent take-over in Jerusalem. Acts 6.14 exhibits a somewhat developed form of polemic (chapter 4). A perspective for discovering the unity of Lk 21 and the development of its thought is provided by the realization that Luke is concerned there with a distancing of Christians from any interest in insurrection and in particular form any interest in seeking to realize their eschatology by means of an armed attack on Jerusalem (chapter 5)