arXiv subjects

Steffen Pottel

Publications and source records attributed to Steffen Pottel.

10 recordsLinked to original sources

arXiv2024

On the Perturbative Quantization of Einstein-Hilbert Gravity Embedded in a Higher Derivative Model II

In a previous paper we presented the renormalization of Einstein-Hilbert gravity under inclusion of higher derivative terms and proposed a projection down to the physical state space of Einstein-Hilbert. In the present paper we describe this procedure in more detail via decomposing the original double-pole field $h^{μν}$ in the bilinear field sector into a massless and a massive spin two field. Those are associated with the poles at zero mass resp. at non-zero mass of $h$ in the tree approximation. We show that the massive fields have no poles in higher orders hence do not correspond to particles. $S$-matrix unitarity is violated only in tree approximation. On the way to these results we derive finiteness properties which are valid in the Landau gauge. Those simplify the renormalization group analysis of the model considerably. We also establish a rigid Weyl identity which represents a proper substitute for a Callan-Symanzik equation in flat spacetime.

hep-th↗

arXiv2021

Lower bounds on mixing norms for the advection diffusion equation in $\mathbb{R}^d$

An algebraic lower bound on the energy decay for solutions of the advection-diffusion equation in $\mathbb{R}^d$ with $d=2,3$ is derived using the Fourier splitting method. Motivated by a conjecture on mixing of passive scalars in fluids, a lower bound on the $L^2-$ norm of the inverse gradient of the solution is obtained via gradient estimates and interpolation.

math.AP↗

arXiv2021

A BPHZ Theorem in Configuration Space

The concept of BPHZ renormalization is translated into configuration space. After deriving the counterpart for the regularizing Taylor subtraction, a new version of Zimmermann's convergence theorem by means of the forest formula is proved. Furthermore, a sufficient condition on the algebraic decay of the integrand is formulated such that the constant coupling limit exists in the new setting.

math-ph↗

arXiv2021

On the Perturbative Quantization of Einstein-Hilbert Gravity Embedded in a Higher Derivative Model

In a perturbative approach Einstein-Hilbert gravity is quantized about a flat background. In order to render the model power counting renormalizable, higher order curvature terms are added to the action. They serve as Pauli-Villars type regulators and require an expansion in the number of fields in addition to the standard expansion in the number of loops. Renormalization is then performed within the BPHZL scheme, which provides the action principle to construct the Slavnov-Taylor identity and invariant differential operators. The final physical state space of the Einstein-Hilbert theory is realized via the quartet mechanism of Kugo and Ojima. Renormalization group and Callan-Symanzik equation are derived for the Green functions and, formally, also for the $S$-matrix.

hep-th↗

arXiv2021

Configuration Space BPHZ Renormalization on Analytic Spacetimes

A configuration space version of BPHZ renormalization is proved in the realm of perturbative algebraic quantum field theory. All arguments are formulated entirely in configuration space so that the range of application is extended to analytic spacetimes. Further the relation to the momentum space method is established. In the course of that, it is necessary to study the limit of constant coupling.

math-ph↗

arXiv2020

Scheduling activities with time-dependent durations and resource consumptions

In this paper we study time-dependent scheduling problems where activities consume a resource with limited availability. Activity durations as well as resource consumptions are assumed to be time-dependent and the resource can be replenished between activities. Because of the interaction of time-dependent activity durations and resource consumptions, scheduling policies based on starting all activities as early as possible may fail due to unnecessarily high resource consumptions. We propose a dynamic discretization discovery algorithm that generates a partially time-expanded network during the search. We propose preloading techniques allowing to significantly reduce the computational effort if the approach is embedded in an iterative solution procedure that frequently evaluates activity sequences that start with the same activities. We evaluate our approaches on a case of routing a fleet of electric vehicles in which vehicles can recharge batteries during the route.

cs.DS↗

arXiv2019

Normal Products and Zimmermann Identities in Configuration Space BPHZ Renormalization

The notion of normal products, a generalization of Wick products, is derived with respect to BPHZ renormalization formulated entirely in configuration space. Inserted into time-ordered products, normal products admit the limit of coinciding field operators, which constitute the product. The derivation requires the introduction of Zimmermann identities, which relate field monomials or renormalization parts with differing subtraction degree. Furthermore, we calculate the action of wave operators on elementary fields inserted into time-ordered products, exploiting the properties of normal products.

math-ph↗

arXiv2017

BPHZ Renormalization in Configuration Space for the $\mathcal{A}^4$-Model

Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.

hep-th↗

arXiv2016

Conjugate variables in quantum field theory and a refinement of Paulis theorem

For the case of spin zero we construct conjugate pairs of operators on Fock space. On states multiplied by polarization vectors coordinate operators Q conjugate to the momentum operator P exist. The massive case is derived from a geometrical quantity, the massless case is realized by taking the limit mass going to zero on the one hand, on the other from conformal transformations. Crucial is the norm problem of the states on which the Q's act: they determine eventually how many independent conjugate pairs exist. It is intriguing that light wedge variables and hence the wedge-local case seems to be preferred.

hep-th↗

arXiv2016

Learning a Deep Model for Human Action Recognition from Novel Viewpoints

Recognizing human actions from unknown and unseen (novel) views is a challenging problem. We propose a Robust Non-Linear Knowledge Transfer Model (R-NKTM) for human action recognition from novel views. The proposed R-NKTM is a deep fully-connected neural network that transfers knowledge of human actions from any unknown view to a shared high-level virtual view by finding a non-linear virtual path that connects the views. The R-NKTM is learned from dense trajectories of synthetic 3D human models fitted to real motion capture data and generalizes to real videos of human actions. The strength of our technique is that we learn a single R-NKTM for all actions and all viewpoints for knowledge transfer of any real human action video without the need for re-training or fine-tuning the model. Thus, R-NKTM can efficiently scale to incorporate new action classes. R-NKTM is learned with dummy labels and does not require knowledge of the camera viewpoint at any stage. Experiments on three benchmark cross-view human action datasets show that our method outperforms existing state-of-the-art.

cs.CV↗