Search results for "Formalism"
showing 10 items of 357 documents
Positivism, Legal Validity, and the Separation of Law and Morals
2014
The essay discusses the import of the separability thesis both for legal positivism and for contemporary legal practice. First, the place of the separability thesis in legal positivism will be explored, distinguishing between “standard positivism” and “post-Hartian positivism.” Then I will consider various kinds of relations between law and morality that are worthy of jurisprudential interest, and explore, from a positivist point of view, what kind of relations between law and morality must be rejected, what kind of such relations should be taken into account, and what kind of such relations are indeed of no import at all. The upshot of this analysis consists in highlighting the distinction…
Semiclassical geons at particle accelerators
2014
We point out that in certain four-dimensional extensions of general relativity constructed within the Palatini formalism stable self-gravitating objects with a discrete mass and charge spectrum may exist. The incorporation of nonlinearities in the electromagnetic field may effectively reduce their mass spectrum by many orders of magnitude. As a consequence, these objects could be within (or near) the reach of current particle accelerators. We provide an exactly solvable model to support this idea.
Renormalisation group improvement in the stochastic formalism
2019
We investigate compatibility between the stochastic infrared (IR) resummation of light test fields on inflationary spacetimes and renormalisation group running of the ultra-violet (UV) physics. Using the Wilsonian approach, we derive improved stochastic Langevin and Fokker-Planck equations which consistently include the renormalisation group effects. With the exception of stationary solutions, these differ from the naive approach of simply replacing the classical potential in the standard stochastic equations with the renormalisation group improved potential. Using this new formalism, we exemplify the IR dynamics with the Yukawa theory during inflation, illustrating the differences between …
Brane-world and loop cosmology from a gravity–matter coupling perspective
2015
We show that the effective brane-world and the loop quantum cosmology background expansion histories can be reproduced from a modified gravity perspective in terms of an $f(R)$ gravity action plus a $g(R)$ term non-minimally coupled with the matter Lagrangian. The reconstruction algorithm that we provide depends on a free function of the matter density that must be specified in each case and allows to obtain analytical solutions always. In the simplest cases, the function $f(R)$ is quadratic in the Ricci scalar, $R$, whereas $g(R)$ is linear. Our approach is compared with recent results in the literature. We show that working in the Palatini formalism there is no need to impose any constrai…
Operator product expansion coefficients in the exact renormalization group formalism
2020
We study how to compute the operator product expansion coefficients in the exact renormalization group formalism. After discussing possible strategies, we consider some examples explicitly, within the $\epsilon$-expansions, for the Wilson-Fisher fixed points of the real scalar theory in $d=4-\epsilon$ dimensions and the Lee-Yang model in $d=6-\epsilon$ dimensions. Finally we discuss how our formalism may be extended beyond perturbation theory.
Non-commutative geometry and covariance: From the quantum plane to quantum tensors
1994
Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.
Pinch technique and the Batalin-Vilkovisky formalism
2002
In this paper we take the first step towards a non-diagrammatic formulation of the Pinch Technique. In particular we proceed into a systematic identification of the parts of the one-loop and two-loop Feynman diagrams that are exchanged during the pinching process in terms of unphysical ghost Green's functions; the latter appear in the standard Slavnov-Taylor identity satisfied by the tree-level and one-loop three-gluon vertex. This identification allows for the consistent generalization of the intrinsic pinch technique to two loops, through the collective treatment of entire sets of diagrams, instead of the laborious algebraic manipulation of individual graphs, and sets up the stage for the…
Connections and geodesics in the space of metrics
2015
We argue that the exponential relation $g_{\mu\nu} = \bar{g}_{\mu\rho}\big(\mathrm{e}^h\big)^\rho{}_\nu$ is the most natural metric parametrization since it describes geodesics that follow from the basic structure of the space of metrics. The corresponding connection is derived, and its relation to the Levi-Civita connection and the Vilkovisky-DeWitt connection is discussed. We address the impact of this geometric formalism on quantum gravity applications. In particular, the exponential parametrization is appropriate for constructing covariant quantities like a reparametrization invariant effective action in a straightforward way. Furthermore, we reveal an important difference between Eucli…
Higher Order Action for the Interaction of the String with the Dilaton
1994
The theory of the string in interaction with a dilaton background field is analyzed. In the action considered, the metric in the world sheet of the string is the induced metric, and the theory presents second order time derivatives. The canonical formalism is developed and it is showed that first and second class constraints appear. The degrees of freedoom are the same than for the free bosonic string. The light cone gauge is used to reduce to the physical modes and to compute the physical hamiltonian.
Planck scale physics and topology change through an exactly solvable model
2014
We consider the collapse of a charged radiation fluid in a Planck-suppressed quadratic extension of General Relativity (GR) formulated à la Palatini. We obtain exact analytical solutions that extend the charged Vaidya-type solution of GR, which allows to explore in detail new physics at the Planck scale. Starting from Minkowski space, we find that the collapsing fluid generates wormholes supported by the electric field. We discuss the relevance of our findings in relation to the quantum foam structure of space–time and the meaning of curvature divergences in this theory.