5,945 research outputs found
One-loop quantum gravity from a worldline viewpoint
No full textWe develop a worldline approach to quantum gravity in D =4. Using the background field method we consider the covariantly gauge fixed Einstein-Hilbert action with cosmological constant, and find a worldline representation of the differential operators identified by its quadratic approximation. We test it by computing the correct one-loop divergencies. Alternative worldline methods, such as the use of the O(4) spinning particle that is known to describe correctly the propagation of a massless spin 2 particle in D = 4, find obstructions in the coupling to an arbitrary background metric, apparently preventing a more extensive use in perturbative descriptions of quantum gravity. We expect that our model might simplify calculations of one-loop amplitudes with respect to standard quantum field theoretical methods
Massive and massless higher spinning particles in odd dimensions
No full textAbstract: We study actions for massive bosonic particles of higher spins by dimensionally reducing an action for massless particles. For the latter we take a model with a SO(N) extended local supersymmetry on the worldline, that is known to describe massless (confor- mal) particles of higher spins in flat spacetimes of even dimensions. Dimensional reduction produces an action for massive spinning particles in odd dimensions. The field equations that emerge in a quantization `a la Dirac are shown to be equivalent to the Fierz-Pauli ones. The massless limit generates a multiplet of massless states with higher spins, whose first quantized field equations have a geometric form with fields belonging to various types of Young tableaux. These geometric equations can be partially integrated to show their equiv- alence with the standard Fronsdal-Labastida equations. We covariantize our model to check whether an extension to curved spacetimes can be achieved. Restricting to (A)dS spaces, we find that the worldline gauge algebra becomes nonlinear, but remains first class. This guar- antees consistency on such backgrounds. A light cone analysis confirms the presence of the expected propagating degrees of freedom. A covariant analysis is worked out explicitly for the massive case, which is seen to give rise to the Fierz-Pauli equations extended to (A)dS spaces. It is worth noting that in D = 3 the massless limit of our model with N → ∞ has the same field content of the Vasiliev’s theory that accommodates each spin exactly once
Audiomobiles, Sculptures and Conundrums
No full textRoberto Gerhard was a pioneer of electronic music in England creating a number of substantial concert, theatre and radio works from as early as 1954. Gerhard’s electronic music is one of the richest repositories for understanding the development of the composer’s late compositional technique. Apart from the Symphony no.3, ‘Collages’, none of Gerhard’s electronic music is published. This paper will discuss aspects of Gerhard’s electronic music, focusing on Audiomobiles (1958-59) and Sculptures (1963)
Gauge-invariant coefficients in perturbative quantum gravity
No full textHeat kernel methods are useful for studying properties of quantum gravity. We recompute the first three heat kernel coefficients in perturbative quantum gravity with cosmological constant to ascertain which ones are correctly reported in the literature. They correspond to the counterterms needed to renormalize the one-loop effective action in four dimensions. They may be evaluated at arbitrary dimensions D, in which case they identify only a subset of the divergences appearing in the effective action for . Generically, these coefficients depend on the gauge-fixing choice adopted in quantizing the Einstein–Hilbert action. However, they become gauge-invariant once evaluated on-shell, i.e. using Einstein’s equations with cosmological constant. Thus, we identify these gauge invariant coefficients and use them as a benchmark for testing alternative approaches to perturbative quantum gravity. One of these approaches describes the graviton in first-quantization through the spinning particle, characterized by four supersymmetries on the worldline and a set of worldline gauge invariances. This description has been used for computing the gauge-invariant coefficients as well. We verify their correctness at , but find a mismatch at arbitrary D when comparing with the benchmark fixed previously. We interpret this result as signaling that the path integral quantization of the spinning particle should be amended. We perform this task by fixing the correct counterterm that must be used in the worldline path integral quantization of the spinning particle to make it consistent in arbitrary dimensions
Extended SUSY quantum mechanics: transition amplitudes and path integrals
No full textQuantum mechanical models with extended supersymmetry find interesting
applications in worldline approaches to relativistic field theories. In this
paper we consider one-dimensional nonlinear sigma models with O(N) extended
supersymmetry on the worldline, which are used in the study of higher spin
fields on curved backgrounds. We calculate the transition amplitude for
euclidean times (i.e. the heat kernel) in a perturbative expansion, using both
canonical methods and path integrals. The latter are constructed using three
different regularization schemes, and the corresponding counterterms that
ensure scheme independence are explicitly identified
Local unit invariance, back-reacting tractors and the cosmological constant problem
No full textWhen physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension
Quantum theory of massless (p, 0)-forms
No full textWe describe the quantum theory of massless (p,0)-forms that satisfy a suitable holomorphic generalization of the free Maxwell equations on Kaehler spaces. These equations arise by first-quantizing a spinning particle with a U(1)-extended local supersymmetry on the worldline. Dirac quantization of the spinning particle produces a physical Hilbert space made up of (p,0)-forms that satisfy holomorphic Maxwell equations coupled to the background Kaehler geometry, containing in particular a charge that measures the amount of coupling to the U(1) part of the U(d) holonomy group of the d-dimensional Kaehler space. The relevant differential operators appearing in these equations are a twisted exterior holomorphic derivative and its hermitian conjugate (twisted Dolbeault operators with charge q). The particle model is used to obtain a worldline representation of the one-loop effective action of the (p,0)-forms. This representation allows to compute the first few heat kernel coefficients contained in the local expansion of the effective action and to derive duality relations between (p,0) and (d-p-2,0)-forms that include a topological mismatch appearing at one-loop
Effective action for higher spin fields on (A)dS backgrounds
No full textWe study the one loop effective action for a class of higher spin fields by using a first-quantized description. The latter is obtained by considering spinning particles, characterized by an extended local supersymmetry on the worldline, that can propagate consistently on conformally flat spaces. The gauge fixing procedure for calculating the worldline path integral on a loop is delicate, as the gauge algebra contains nontrivial structure functions. Restricting the analysis on (A)dS backgrounds simplifies the gauge fixing procedure, and allows us to produce a useful representation of the one loop effective action. In particular, we extract the first few heat kernel coefficients for arbitrary even spacetime dimension D and for spin S identified by a curvature tensor with the symmetries of a rectangular Young tableau of D/2 rows and [S] columns
Gravity, two times, tractors, Weyl invariance, and six-dimensional quantum mechanics
No full textFefferman and Graham showed some time ago that four-dimensional conformal geometries could be analyzed in terms of six-dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently, it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit systems. Strikingly, Einstein’s equations are then equivalent to the existence of a parallel scale tractor (a six-component vector subject to a certain first order covariant constancy condition at every point in four-dimensional spacetime). These results suggest a six-dimensional description of four-dimensional physics, a viewpoint promulgated by the 2 times physics program of Bars. The Fefferman-Graham construction relies on a triplet of operators corresponding, respectively, to a curved six-dimensional light cone, the dilation generator and the Laplacian. These form an sp(2) algebra which Bars employs as a first class algebra of constraints in a six-dimensional gauge theory. In this article four-dimensional gravity is recast in terms of six-dimensional quantum mechanics by melding the 2 times and tractor approaches. This parent formulation of gravity is built from an infinite set of six-dimensional fields. Successively integrating out these fields yields various novel descriptions of gravity including a new four-dimensional one built from a scalar doublet, a tractor-vector multiplet and a conformal class of metrics
U(N) spinning particles and higher spin equations on complex manifolds
No full textGuided by a spinning particle model with U(N)-extended supergravity on the worldline we derive higher spin equations on complex manifolds. Their minimal formulation is in term of gauge fields which satisfy suitable constraints. The latter can be relaxed by introducing compensator fields. There is an obstruction to define these systems on arbitrarily curved spaces, just as in the usual theory of higher spin fields, but we show how to couple them to Kahler manifolds of constant holomorphic curvature. Quite interestingly, the first class gauge algebra defining the U(N) particles on these manifolds is quadratic and realizes the zero mode sector of certain nonlinear U(N) superconformal algebras introduced sometimes ago by Bershadsky and Knizhnik in 2D
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