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D. R. Grigore

Publications and source records attributed to D. R. Grigore.

17 recordsLinked to original sources
arXiv2020

Anti-BRST in the Causal Approach

It is known that the elimination of the anomalies in all orders of perturbation theory is an open problem. The constrains given by usual invariance properties and the Wess-Zumino identities are not enough to eliminate the anomalies in the general case of an Yang-Mills theory. So, any new symmetry of the model could restrict further the anomalies and be a solution of the problem. We consider the anti-BRST transform of Ojima in the causal approach and investigate if such new restrictions are obtained. Unfortunately, the result is negative: if we have BRST invariance up to the second order of the perturbation theory, we also have anti-BRST invariance up to the same order. Probably, this result is true in all orders of the perturbation theory. So, anti-BRST transform gives nothing new, and we have to find other ideas to restrict and eventually eliminate the anomalies for a general Yang-Mills theory.

hep-th↗
arXiv2020

Factorization Formulas for Tree Amplitudes

We present a coordinate space version of the factorization formula for the connected tree part of the chronological products. We consider a general framework and then we apply it for the QCD case.

hep-th↗
arXiv2018

Anomaly-Free Gauge Models: A Causal Approach

The gauge invariance of some massless Yang-Mills models can be proved for a large class of groups using Polchinski flow equations approach. In this paper we provide an alternative proof based on the causal approach. The proof is purely algebraic and is based on the analysis of the anomalies. More precisely, one can prove that the anomalies are verifying some consistency equations of Wess-Zumino type. In the massless SU(2) Yang-Mills case, this is enough to prove that they are absent. The same is true for QED.

hep-th↗
arXiv2010

Non-trivial 2+1-Dimensional Gravity

We analyze 2+1-dimensional gravity in the framework of quantum gauge theory. We find that Einstein gravity has a trivial physical subspace which reflects the fact that the classical solution in empty space is flat. Therefore we study massive gravity which is not trivial. In the limit of vanishing graviton mass we obtain a non-trivial massless theory different from Einstein gravity. We derive the interaction from descent equations and obtain the cosmological topologically massive gravity. However, in addition to Einstein and Chern-Simons coupling we need coupling to fermionic ghost and anti-ghost fields and to a vector-graviton field with the same mass as the graviton.

gr-qc↗
arXiv2010

The Interaction of Quantum Gravity with Matter

The interaction of (linearized) gravitation with matter is studied in the causal approach up to the second order of perturbation theory. We consider the generic case and prove that gravitation is universal in the sense that the existence of the interaction with gravitation does not put new constraints on the Lagrangian for lower spin fields. We use the formalism of quantum off-shell fields which makes our computation more straightforward and simpler.

hep-th↗
arXiv2009

From massive gravity to modified general relativity II

We continue our investigation of massive gravity in the massless limit of vanishing graviton mass. From gauge invariance we derive the most general coupling between scalar matter and gravity. We get further couplings beside the standard coupling to the energy-momentum tensor. On the classical level this leads to a further modification of general relativity.

gr-qc↗
arXiv2008

Massive Yang-Mills Fields in Interaction with Gravity

We determine the most general form of the interaction between the gravitational field and an arbitrary Yang-Mills system of fields (massless and massive). We work in the perturbative quantum framework of the causal approach (of Epstein and Glaser) and use a cohomological definition of gauge invariance for both gauge fields. We also consider the case of massive gravity. We discuss the question whether gravity couples to the unphysical degrees of freedom in the Yang-Mills fields.

hep-th↗
arXiv2007

Massive gravity from descent equations

Both massless and massive gravity are derived from descent equations (Wess-Zumino consistency conditions). The massive theory is a continuous deformation of the massless one.

hep-th↗
arXiv1994

Varational Equations and Symmetries in the Lagrangian Formalism

Symmetries in the Lagrangian formalism of arbitrary order are analysed with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second order equations and a scalar field we establish a polynomial structure in the second order derivatives. This structure can be used to make more precise the form of a general symmetry. As an illustration we analyse the case of Lagrangian equations with Poincaré invariance or with universal invariance.

hep-th↗
arXiv1994

Free Fields for Any Spin in 1+2 Dimensions

We construct free fields of arbitrary spin in 1+2 dimensions i.e. free fields for which the one-particle Hilbert space carries a projective isometric irreducible representation of the Poincaré group in 1+2 dimensions. We analyse in detail these representations in the fiber bundle formalism and afterwards we apply Weinberg procedure to construct the free fields. Some comments concerning axiomatic field theory in 1+2 dimensions are also made.

hep-th↗
arXiv1993

Conformal Invariance in Classical Field Theory

A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the action functional can be taken strictly invariant with respect to these transformations. In other words, there does not exists a "Chern-Simons" type Lagrangian for a conformally invariant Lagrangian theory.

hep-th↗