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Register a new userQuantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries
نظرية الحقل الكموني على الخلفيات المنحنية. II. تناسق المكان والزمن
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Arthur Jaffe
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نحن ندرس التناسقات الزمنية-الفضائية في نظرية الحقل الكمي المقيد (بما في ذلك النظريات التفاعلية) على الأماكن الثابتة. نحن نعتبر أولا نظرية الحقل الكمي اليوكليدي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي اللورنتزي على مخطط متوسطي ثابت، ونظرية الحقل الكمي ال
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is generated by one-parameter subgroups which have either self-adjoint or unitary quantizations. We analytically continue the self-adjoint semigroups to one-parameter unitary groups, and thus construct a unitary representation of the isometry group of the associated Lorentzian manifold. The method is illustrated for the example of hyperbolic space, whose Lorentzian continuation is Anti-de Sitter space.
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We study a free scalar field $phi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form $F(Box)phi =0$, where $F$ is a polynomial of the form $F(Box)= prod_i (Box-m_i^2)$ and all masses $m_i$ are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetric energy-momentum tensor and compare it with the canonical energy-momentum tensor when the background is Minkowski spacetime. We also obtain the conserved symplectic current necessary for quantisation and briefly discuss the issue of negative energy versus negative norm and its relation to Reflection Positivity in Euclidean treatments. We study, without assuming spherical symmetry, the possible existence of finite energy static solutions of the scalar equations, in static or stationary background geometries. Subject to various assumptions on the potential, we establish non-existence results including a no-scalar-hair theorem for static black holes. We consider Pais-Uhlenbeck field theories in a cosmological de Sitter background, and show how the Hubble friction may eliminate what would otherwise be unstable behaviour when interactions are included.
In four spacetime dimensions, all ${cal N} =1$ supergravity-matter systems can be formulated in the so-called $mathsf{U}(1)$ superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background $mathsf{U}(1)$ superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields $ell_{(alpha_1 dots alpha_m) ({dot alpha}_1 dots {dot alpha}_n)}$, with $m$ and $n$ non-negative integers, $m+n>0$, and elaborate on their significance in the following cases: (i) $m=n=1$; (ii) $m-1=n=0$; and (iii) $m=n>1$. The (conformal) Killing vector superfields $ell_{alpha dot alpha}$ generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields $ell_{alpha }$ generate extended (conformal) supersymmetry transformations. The (conformal) Killing tensor superfields with $m=n>1$ prove to generate all higher symmetries of the (massless) massive Wess-Zumino operator.
Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of the Coriolis force and spin-vorticity coupling in generating the chiral vortical effect (CVE). We also show that the CVE is an intrinsic phenomenon of a rotating chiral fluid, and thus independent of observers frame.
In this paper we use the AdS/CFT correspondence to refine and then establish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any long-range bulk gauge symmetry leads to a global symmetry in the boundary CFT, whose consistency requires the existence of bulk dynamical objects which transform in all finite-dimensional irreducible representations of the bulk gauge group. We mostly assume that all internal symmetry groups are compact, but we also give a general condition on CFTs, which we expect to be true quite broadly, which implies this. We extend all of these results to the case of higher-form symmetries. Finally we extend a recently proposed new motivation for the weak gravity conjecture to more general gauge groups, reproducing the convex hull condition of Cheung and Remmen. An essential point, which we dwell on at length, is precisely defining what we mean by gauge and global symmetries in the bulk and boundary. Quantum field theory results we meet while assembling the necessary tools include continuous global symmetries without Noether currents, new perspectives on spontaneous symmetry-breaking and t Hooft anomalies, a new order parameter for confinement which works in the presence of fundamental quarks, a Hamiltonian lattice formulation of gauge theories with arbitrary discrete gauge groups, an extension of the Coleman-Mandula theorem to discrete symmetries, and an improved explanation of the decay $pi^0togamma gamma$ in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in $d+1$ dimensions with horizon topology $mathbb{T}^ptimes mathbb{S}^{d-p-1}$.
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