相关论文: On Mode Regularization of the Configuration Space …

The proper definition and evaluation of the configuration space path integral for the motion of a particle in curved space is a notoriously tricky problem. We discuss a consistent definition which makes use of an expansion in Fourier sine…

We compute the perturbative short-time expansion for the transition amplitude of a particle in curved space time, by employing Dimensional Regularization (DR) to treat the divergences which occur in some Feynman diagrams. The present work…

We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general…

A simple, often invoked, regularization scheme of quantum mechanical path integrals in curved space is mode regularization: one expands fields into a Fourier series, performs calculations with only the first $M$ modes, and at the end takes…

By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved…

We discuss the quantisation of a class of string cosmology models that are characterized by scale factor duality invariance. We compute the amplitudes for the full set of classically allowed and forbidden transitions by applying the reduce…

Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…

In this talk we discuss the quantisation of a class of string cosmology models characterised by scale factor duality invariance. The amplitudes for the full set of classically allowed and forbidden transitions are computed by applying the…

We investigate the non-perturbative quantization of phantom and ghost degrees of freedom by relating their representations in definite and indefinite inner product spaces. For a large class of potentials, we argue that the same physical…

Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…

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…

We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…

p-Adic generalization of the Feynman path integrals in quantum mechanics is considered. The probability amplitude for a particle in a constant field is calculated. Path integrals over p-adic space have the same form as those over R.

We derive a path integral expression for the transition amplitude in 1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization leads to a formulation in terms of gauge invariant but curvilinear variables.…

In Euclidean path integrals, quantum mechanical tunneling amplitudes are associated with instanton configurations. We explain how tunneling amplitudes are encoded in real-time Feynman path integrals. The essential steps are borrowed from…

The computation of anomalies in quantum field theory may be carried out by evaluating path integral Jacobians, as first shown by Fujikawa. The evaluation of these Jacobians can be cast in the form of a quantum mechanical problem, whose…

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…

A general procedure for deriving the path integral representation of a transition amplitude on the gauge orbit space having a non-trivial topology is proposed. The path integral formula appears to be modified by including trajectories…

Reduction to physical degrees of freedom before quantization leads to predictions for one-loop amplitudes in quantum cosmology in the presence of boundaries which disagree with the results obtained from Faddeev-Popov theory and…

A coarse graining technique akin to block spin transformations that groups together fiducial cells in a homogeneous and isotropic universe has been recently developed in the context of loop quantum cosmology. The key technical ingredient…