3,842 research outputs found
A C*-Algebra for Quantized Principal U(1)-Connections on Globally Hyperbolic Lorentzian Manifolds
No full textThe aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes of connections. The C*-algebra we construct generalizes the usual CCR-algebras, since, contrary to the standard field-theoretic models, it is based on a presymplectic Abelian group instead of a symplectic vector space. We prove a no-go theorem according to which neither this functor, nor any of its quotients, satisfies the strict axioms of general local covariance. As a byproduct, we prove that a morphism violates the locality axiom if and only if a certain induced morphism of cohomology groups is non-injective. We show then that, fixing any principal U(1)-bundle, there exists a suitable category of subbundles for which a quotient of our functor yields a quantum field theory in the sense of Haag and Kastler. We shall provide a physical interpretation of this feature and we obtain some new insights concerning electric charges in locally covariant quantum field theory
Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss' law
No full textWe quantise the massless vector potential A of electromagnetism in the presence of a classical electromagnetic (background) current, j, in a generally covariant way on arbitrary globally hyperbolic spacetimes M. By carefully following general principles and procedures we clarify a number of topological issues. First we combine the interpretation of A as a connection on a principal U(1)-bundle with the perspective of general covariance to deduce a physical gauge equivalence relation, which is intimately related to the Aharonov-Bohm effect. By Peierls' method
we subsequently find a Poisson bracket on the space of local, affine observables of the theory. This Poisson bracket is in general degenerate, leading to a quantum theory with non-local behaviour. We show that this non-local behaviour can be fully explained in terms of Gauss' law.
Thus our analysis establishes a relationship, via the Poisson bracket, between the Aharonov-Bohm effect and Gauss' law -- a relationship which seems to have gone unnoticed so far. Furthermore, we find a formula for the space of electric monopole charges in terms of the topology of the
underlying spacetime. Because it costs little extra effort, we emphasise the cohomological perspective and derive our results for general p-form fields A (p<dim(M)), modulo exact field. In conclusion we note that the theory is not locally covariant, in the sense of Brunetti-Fredenhagen-Verch. It is not possible to obtain such a theory by dividing out the centre of the algebras, nor is it physically desirable to do so. Instead we argue that electromagnetism forces us to weaken the axioms of the framework of local covariance, because the failure of locality is physically well-understood and should be accommodated
The Generalised Principle of Perturbative Agreement and the Thermal Mass
No full textThe principle of perturbative agreement, as introduced by Hollands and Wald, is a renormalization condition in quantum field theory on curved spacetimes. This principle states that the perturbative and exact constructions of a field theoretic model given by the sum of a free and an exactly tractable interaction Lagrangian should agree. We develop a proof of the validity of this principle in the case of scalar fields and quadratic interactions without derivatives, which differs in strategy from the one given by Hollands and Wald for the case of quadratic interactions encoding a change of metric. Thereby, we profit from the observation that, in the case of quadratic interactions, the composition of the inverse classical Møller map and the quantum Møller map is a contraction exponential of a particular type. Afterwards, we prove a generalisation of the principle of perturbative agreement and show that considering an arbitrary quadratic contribution of a general interaction either as part of the free theory or as part of the perturbation gives equivalent results. Motivated by the thermal mass idea, we use our findings to extend the construction of massive interacting thermal equilibrium states in Minkowski spacetime developed by Fredenhagen and Lindner to the massless case. In passing, we also prove a property of the construction of Fredenhagen and Lindner which was conjectured by these authors
Approximate KMS States for Scalar and Spinor Fields in Friedmann–Robertson–Walker Spacetimes
No full textWe construct and discuss Hadamard states for both scalar and Dirac spinor fields in a large class of spatially flat Friedmann–Robertson– Walker spacetimes characterised by an initial phase either of exponential or of power-law expansion. The states we obtain can be interpreted as being in thermal equilibrium at the time when the scale factor a has a specific value a = a0. In the case a0 = 0, these states fulfil a strict KMS condition on the boundary of the spacetime, which is either a cosmologi- cal horizon or a Big Bang hypersurface. Furthermore, in the conformally invariant case, they are conformal KMS states on the full spacetime. How- ever, they provide a natural notion of an approximate KMS state also in the remaining cases, especially for massive fields. On the technical side, our results are based on a bulk-to-boundary reconstruction tech- nique already successfully applied in the scalar case and here proven to be suitable also for spinor fields. The potential applications of the states we find range over a broad spectrum, but they appear to be suited to discuss in particular thermal phenomena such as the cosmic neutrino background or the quantum state of dark matter
Cosmological Applications of Algebraic Quantum Field Theory
No full textQuantum field theory on curved spacetime is a generalisation of quantum field theory in flat spacetime which is expected to be the proper fundamental description of non-trivial physical phenomena in the presence of a spacetime curvature which is large but below Planck scale. Two prominent physical situations which fall under this characterisation are phenomena both in the vicinity of black holes and in the early universe. Focusing on the latter, we review several applications of algebraic quantum field theory on curved spacetimes to cosmology, as well as foundational results and constructions on which these applications are based. On the foundational side, we collect several proposals to construct Hadamard states on cosmological spacetimes, as this class of states is believed to encompass all physically meaningful states in quantum field theory on curved spacetimes. Afterwardswe consider the solution theory of the semiclassical Einstein equation, quote a theorem of existence and uniqueness of solutions to this equation and indicate directions to go beyond the semiclassical Einstein equation. Then we highlight how the observed cosmological expansion may be understood qualitatively and quantitatively in this framework, before we discuss the quantization of perturbations in inflation in the context of algebraic quantum field theory. In the latter subject, the starting point is the assumption that the classical, rather than the semiclassical, Einstein equation is satisfied.We close this chapter briefly discussing how one may generalise the analysis of perturbations in inflation by allowing for spacetimes backgrounds which solve the semiclassical Einstein equations
The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor
No full textAn analytic regularisation scheme on curved space-times with applications to cosmological space-times
No full textWe develop a renormalisation scheme for time-ordered products in interacting field theories on curved space-times that consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This scheme is directly applicable to space-times with Lorentzian signature, manifestly generally covariant, invariant under any space-time isometries present, and constructed to all orders in perturbation theory. Moreover, the scheme correctly captures the nongeometric state-dependent contribution of Feynman amplitudes, and it is well suited for practical computations. To illustrate this last point, we compute explicit examples on a generic curved space-time and demonstrate how momentum space computations in cosmological space-times can be performed in our scheme. In this work, we discuss only scalar fields in four space-time dimensions, but we argue that the renormalisation scheme can be directly generalised to other space-time dimensions and field theories with higher spin as well as to theories with local gauge invariance
Cosmological perturbation theory and quantum gravity
No full textIt is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well
Thomas of Marga's Monastic History and Other Texts
No full textBedjan here offers in his customary manner (i.e. in fully vocalized east Syriac script) several texts: Thomas of Marga’s Monastic History of Bet ‘Abe (also known as the Book of Governors), ‘Ishodnah’s Book of Monastery Founders, Homilies on Joseph by Narsai, and a collection of texts from Leo the Great (the Tome), Nestorius, Sahdona (Martyrius), and the Testament of St. Ephrem (in a different redaction than those previously published). The volume is prefaced with an introduction in French. This range of materials will be of interest to every reader concerned with the theology and history of Syriac Christianity.Includes introduction in French
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