Related papers: Trace Anomaly in Geometric Discretization
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
An interpretation of the gauge anomaly of the two-dimensional multi-phase sigma model is presented in terms of an obstruction to the existence of a topological defect network implementing a local trivialisation of the gauged sigma model.
This paper is a summary of my talk at SPIE2013. The organizers were kind enough to invite me to talk about anything I wanted, and I chose to bring up the notion of higher order complementarity and the fact that it may not be monotonic. I…
It is pointed out that every renormalizable field theory has a symmetry which is hidden in plain sight. In all practical cases, it is also broken softly, either explicitly or spontaneously. The soft explicit breaking mass terms may be…
I identify the class of even-dimensional conformal field theories that is most similar to two-dimensional conformal field theory. In this class the formula, elaborated recently, for the irreversibility of the renormalization-group flow…
The field-antifield quantization method is used to calculate the trace anomaly for a massless scalar field in a curved background, by means of the zeta function regularization procedure.
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of…
Using the results of the calculation of the one-loop effective action (E. Elizalde et al , Phys.Rev. D49 (1994) 2852), we find the trace anomaly for most general conformally invariant 2D dilaton coupled scalar-dilaton system (the…
In this work we develop a discrete trace theory that spans non-conforming hybrid discretization methods and holds on polytopal meshes. A notion of a discrete trace seminorm is defined, and trace and lifting results with respect to a…
The spherically symmetric reduction of higher dimensional Einstein-scalar theory leads to lower dimensional dilatonic gravity with dilaton coupled scalar (for example, from 4D to 2D system). We calculate trace anomaly and anomaly induced…
Paying attention to conformal invariance as the invariance under local transformations of units of measure, we take a conformal invariant quantum field as a quantum matter theory in which one has the freedom to choose the values of units of…
Two examples, not connected at present, from author's papers (Nuovo Cim., 1992, v.105A, p.77 [hep-th/0207210] and GRG, 1999, v.31, p.1431 [gr-qc/0207017]) are considered here in which a physical model has discrete symmetries and additional…
We present a semiclassical theory for electron drag between two parallel two-dimensional electron systems in a strong magnetic field, which provides a transparent picture of the most salient qualitative features of anomalous drag phenomena…
A recently proposed effective action for the trace anomaly describes a tensor-scalar theory that is weakly coupled up to a certain high energy scale, where it becomes strongly interacting. Its ultraviolet completion is obtained by coupling…
The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED…
The conformally invariant symmetric traceless field $A$ is considered. In four dimensions it possesses a scalar gauge invariance to which we provide a conformally invariant gauge fixing equation. A field strength $F$ is built upon $A$, its…
Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric…
We consider the quantum effects of matter fields in scalar-tensor theories and clarify the role of trace anomaly when switching between conformally related `frames'. We exploit the property that the couplings between the scalar and the…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…