Related papers: The Worldline Path Integral Approach to Feynman Gr…
The worldline formalism offers an alternative framework to the standard diagrammatic approach in quantum field theory, grounded in first-quantized relativistic path integrals. Over recent decades, this formalism has attracted growing…
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…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
In nuclear and particle physics one is often faced with problems where perturbation theory is not applicable. An example of this is the description of bound states. Therefore, an exact solution of field theory to all orders is an…
We show that the Feynman path integral together with the Schr\"odinger representation gives rise to a rigorous and functorial quantization scheme for linear and affine field theories. Since our target framework is the general boundary…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
It is wellknown that the Feynman kernel for the free particle on the half-line can be expressed as a sum over classical paths if we take the contribution from the reflected path into account. The minus sign for the reflected path needs to…
As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates…
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…
Feynman's path integral formulation arose from his attempt to incorporate the Lagrangian framework into quantum mechanics, offering what he regarded as a more fundamental perspective than the Hamiltonian approach, particularly in the…
We summarize recent progress in applying the worldline formalism to the analytic calculation of one-loop N-point amplitudes. This string-inspired approach is well-adapted to avoiding some of the calculational inefficiencies of the standard…
The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra…
We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
The worldline method is a powerful numerical path-integral framework for computing Casimir and Casimir-Polder energies. An important challenge arises when one desires derivatives of path-integral quantities--standard finite-difference…
We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant…
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…
The Feynman path integral does not allow a "one real path" interpretation, because amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, "all paths happen", is not a useful or informative account. In this…