Related papers: Path-Integral Measures in Higher-Derivative Gravit…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
We provide two independent systematic methods of performing $D$-dimensional physical-state sums in gauge theory and gravity in such a way so that spurious light-cone singularities are not introduced. A natural application is to generalized…
We define a discrete gauge-invariant Yang-Mills-Higgs action on spacetime simplicial meshes. The formulation is a generalization of classical lattice gauge theory, and we prove consistency of the action in the sense of approximation theory.…
A positive, diffeomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with the generalized measures of Ashtekar and Lewandowski…
A general form for the equation of motion for higher-curvature gravity is obtained. The interesting feature of the analysis is that it can handle Lagrangians which contain non-minimal kinetic scalar couplings. Certain subtle features, which…
A new way of orthogonalizing ensembles of vectors by "lifting" them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
The variational methods implemented on a quadratic Yang-Mills type Lagrangian yield two sets of equations interpreted as the field equations and the energy-momentum tensor for the gravitational field. A covariant condition is imposed on the…
We provide a higher dimensional extension of the gravitational decoupling method. This extended method allows to obtain new analytic and well behaved solutions that could be associated to higher dimensional stellar distributions.…
This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
We study the properties of several proximity measures for the vertices of weighted multigraphs and multidigraphs. Unlike the classical distance for the vertices of connected graphs, these proximity measures are applicable to weighted…
Path integrals can be rigorously defined only in low dimensional systems where the small distance limit can be taken. Particularly non-trivial models in more than four dimensions can only be handled with considerable amount of speculation.…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
The relationship between various methods to calculate the physical degrees of freedom for gauge invariant systems of a general form is established. The set of hidden parameters caused for the superfluous degrees of freedom is revealed.
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
We present a formalism to determine the imaginary part of a general chiral model in the derivative expansion. Our formalism is based on the worldline path integral for the covariant current that can be given in an explicit chiral and gauge…
We investigate path integral quantization of two versions of unimodular gravity. First a fully diffeomorphism-invariant theory is analyzed, which does not include a unimodular condition on the metric, while still being equivalent to other…
We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property,…