Related papers: A Path (Integral) to Scale Invariance
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
In this paper path integration in two- and three-dimensional spaces of constant curvature is discussed: i.e.\ the flat spaces $\bbbr^2$ and $\bbbr^3$, the two- and three-dimensional sphere and the two- and three dimensional pseudosphere.…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber bundle, the independence of the formal path…
The path-integral approach to cosmology consists in the computation of transition amplitudes between states of the quantum geometry of the universe. In the past, the concrete computation of these transitions amplitudes has been performed in…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
We quantize scalar fluctuations in 1+1 dimensions above a classical background kink. The properties of the effective action for the corresponding classical field are studied with an exact functional method, alternative to exact Wilsonian…
We present an integral formalism for constructing scheme transformations in a quantum field theory. We apply this to generate several new useful scheme transformations. A comparative analysis is given of these scheme transformations in…
The propagator of a spinning particle in external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has different solutions in even and odd dimensions. In even dimensions the representation is…
The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. The realizations of scale invariance which are considered, are in the context of a gravitational theory where the action, in the first…
We give two novel proofs that the path integral and stochastic quantizations of generic scalar Euclidean quantum field theories are equivalent. Our proofs rely on Taylor interpolations indexed by forests, in the fashion of constructive…
We study the implications of scale invariance in four-dimensional quantum field theories. Imposing unitarity, we find that infinitely many matrix elements vanish in a suitable kinematical configuration. This vanishing is a nontrivial…
Invited talk given at the ``International Workshop on `Symmetry Methods in Physics' in memory of Ya.\ A.\ Smorodinsky, 5--10 July 1993, Dubna, Russia; to appear in the proceedings. In this contribution I present further results on steps…
Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian…
In this paper we consider an alternative formulation of a class of stochastic wave and master equations with scalar noise that are used in quantum optics for modelling open systems and continuously monitored systems. The reformulation is…
Work belongs to the most basic notions in thermodynamics but it is not well understood in quantum systems, especially in open quantum systems. By introducing a novel concept of work functional along individual Feynman path, we invent a new…
We construct a new topology on the space of stopped paths and introduce a calculus for causal functionals on generic domains of this space. We propose a generic approach to pathwise integration without any assumption on the variation index…
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this…