Related papers: Beyond complex Langevin equations II: a positive r…
A simple integral relation between a complex weight and the corresponding positive distribution is derived by introducing a second complex variable. Together with the positivity and normalizability conditions, this sum rule allows to…
By introducing a second complex variable, the integral relation between a complex density and the corresponding positive distribution is derived. Together with the positivity and normalizability conditions, this sum rule allows to construct…
After a short review of one of proposals to avoid complex stochastic processes in Complex Langevin studies, the recent progress in the former is reported. In particular, the new developments allow now to construct positive and normalizable…
A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several…
Many research programs aiming to deal with the sign problem were proposed since the advent of lattice field theory. Several of these try to achieve this by exploiting properties of analytic functions. This is also the case for our study.…
Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations. This is the well-known sign problem. The complex Langevin approach amounts to effectively construct…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
Recently, Hoshina, Fujii, and Kikukawa pointed out that the naive lattice gauge theory action in Minkowski signature does not result in a unitary theory in the continuum limit, and Kanwar and Wagman proposed alternative lattice actions to…
We investigate lattice simulations of scalar and nonabelian gauge fields in Minkowski space-time. For SU(2) gauge-theory expectation values of link variables in 3+1 dimensions are constructed by a stochastic process in an additional (5th)…
An extension of the Lorentz group that includes generators $\Gamma^\mu$ carrying a space-time index has been previously demonstrated to \emph{explicitly} construct the Minkowski metric \emph{within} the internal group space as a consequence…
In this work, we study linearised gravitational fields on the entire Minkowski space-time including space-like infinity. The generalised conformal field equations linearised about a Minkowski background are utilised for this purpose. In…
Applications of the Path Group (consisting of classes of continuous curves in Minkowski space-time) to gauge theory and gravity are reviewed. Covariant derivatives are interpreted as generators of an induced representation of Path Group.…
Timelike Liouville field theory (also known as imaginary Liouville theory or imaginary Gaussian multiplicative chaos) is expected to describe two-dimensional quantum gravity in a positive-curvature regime, but its path integral is not a…
Feynman's i-epsilon prescription for quantum field theoretic propagators has a quite natural reinterpretation in terms of a slight complex deformation of the Minkowski spacetime metric. Though originally a strictly flat-space result, once…
Many non-Hermitian but PT-symmetric theories are known to have a real positive spectrum. Since the action is complex for there theories, Monte Carlo methods do not apply. In this paper the first field-theoretic method for numerical…
We demonstrate that the positive frequency modes for a complex scalar field in a constant electric field (Schwinger modes), in three different gauges, can be represented as exact Lorentzian worldline path integral amplitudes. Although the…
Two different versions of relativistic Langevin equation in curved spacetime background are constructed, both are manifestly general covariant. It is argued that, from the observer's point of view, the version which takes the proper time of…
A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of…
The problem of finding a positive distribution, which corresponds to a given complex density, is studied. By the requirement that the moments of the positive distribution and of the complex density are equal, one can reduce the problem to…
We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour…