Related papers: Quantum mechanical path integrals in curved spaces…
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…
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…
While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and…
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,…
We construct a path integral based on the coupling of the Liouville action and the Mabuchi K-energy on a one-dimensional complex manifold. To the best of our knowledge this is the first rigorous construction of such an object and this is…
Euclidean quantum-gravity path-integrals are investigated within Regge calculus by computer simulations. The domain of integration is restricted by introducing a lower limit for the fatness of each simplex. We use the standard hypercubic…
We present a derivation of the Schr\"odinger equation for a path integral of a point particle in a space with curvature and torsion which is considerably shorter and more elegant than what is commonly found in the literature.
The very early universe is understood in terms of quantum field theories on curved spacetime, where the classical background spacetime is typically an FLRW cosmology and the quantum fields which propagate on it include gravitational waves…
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex…
Input-output theory is a well-known tool in quantum optics and ubiquitous in the description of quantum systems probed by light. Owing to the generality of the setup it describes, the theory finds application in a wide variety of…
Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the…
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work…
We present a way for calculating the Lagrangian path integral measure directly from the Hamiltonian Schwinger--Dyson equations. The method agrees with the usual way of deriving the measure, however it may be applied to all theories, even…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
According to loop quantum gravity, matter fields must be quantized in a background independent manner. For scalar fields, such a background independent quantization is called polymer quantization and is inequivalent to the standard…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
We show how the path-integral formulation of quantum statistical mechanics can be used to construct practical {\em ab initio} techniques for computing the chemical potential of molecules adsorbed on surfaces, with full inclusion of quantum…
Inspired by the usefulness of local scaling of time in the path integral formalism, we introduce a new kind of hamiltonian path integral in this paper. A special case of this new type of path integral has been earlier found useful in…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection…