相关论文: Trace Anomaly in Geometric Discretization

In this paper we investigate the trace anomaly in a spacetime where single events are de-localized as a consequence of short distance quantum coordinate fluctuations. We obtain a modified form of heat kernel asymptotic expansion which does…

T-Duality is a poorly understood symmetry of the space-time fields of string theory that interchanges long and short distances. It is best understood in the context of toroidal compactification where, loosely speaking, radii of the torus…

We consider the trace anomaly, which results from the integration of the massless conformal fermion field with the background of metric and antisymmetric tensor fields. The non-local terms in the anomaly-induced effective action do not…

We outline the duality between the extraordinary magnetoresistance (EMR), observed in semiconductor-metal hybrids, and non-symmetric gravity coupled to a diffusive $U(1)$ gauge field. The corresponding gravity theory may be interpreted as…

As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form…

A dimensional interpolation between the free energy and conformal anomaly on spheres is derived for free scalar and spinor fields on the basis of standard field theory. The regularisation used is an extension of one by Candelas and…

We lay the foundations for a general approach to nonassociative spectral geometry as an extension of Connes' noncommutative geometry by explaining how to construct finite-dimensional, discrete spectral geometries with exceptional symmetry,…

Due to the non-renormalizability of gravity, the perturbative expansion has sense, say, for its discrete simplicial (Regge calculus) version. A finite-difference form of gravity action has diffeomorphism symmetry at leading order over…

We show that three-dimensional trace anomalies lead to new universal anomalous transport effects on a conformally-flat spacetime with background scalar fields. In contrast to conventional anomalous transports in quantum chromodynamics (QCD)…

The conformal anomaly and anomaly-induced effective action represent useful and economic ways to describe semiclassical contributions to the action of gravity. We discuss the anomaly in the case when the background is formed by metric and…

zeta-regularized traces, resp. super-traces, are defined on a classical pseudo-differential operator A by: tr^Q(A):= f.p.tr(A Q^{-z})_{|_{z=0}}, resp. str^Q(A):= f.p.str(A Q^{-z})_{|_{z=0}}, where f.p. refers to the finite part and Q is an…

Usually, in order to compute an anomaly (be it chiral or trace) with a perturbative method, the lowest significant order is sufficient. With the help of gauge or diffeomorphism invariance it uniquely identifies the anomaly. This note is a…

The use of proper time as a tool for causality implementation in field theory is clarified and extended to allow a manifestly covariant definition of discrete fields proper to be applied in field theory and quantum mechanics. It implies on…

The one-loop structure of the trace anomaly is investigated using different regularizations and renormalization schemes: dimensional, proper time and Pauli-Villars. The universality of this anomaly is analyzed from a very general…

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces.…

We analyze the semiclassical Einstein equations for quantum scalar fields satisfying modified dispersion relations. We first discuss in detail the renormalization procedure based on adiabatic subtraction and dimensional regularization. We…

The conformal anomaly has well-known ambiguities related to the possible schemes of regularization and renormalization. In case of dimensional regularization, one of the options is to formulate the theory as conformal in the dimension $D…

We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of…

A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…

Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…