Related papers: Is the Polyakov path integral prescription too res…
We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the…
Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them…
Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and…
Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…
Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of…
Previous analysis about the deparametrization and path integral quantization of cosmological models are extended to models which do not admit an intrinsic time. The formal expression for the transition amplitude is written down for the Taub…
We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…
It is explained how first-quantized worldline path integrals can be used as an efficient alternative to Feynman diagrams in the calculation of QED amplitudes and effective actions. The examples include the one-loop photon splitting…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
Performing an nonperturbative path integral for the geometric part of a large class of 2d theories without kinetic term for the dilaton field, the quantum effects from scalar matter fields are treated as a perturbation. When integrated out…
A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the…
We use the worldline formalism to derive master formulas for the one-loop N-photon amplitudes in a plane-wave background, for both scalar and spinor QED. This generalises previous work by Ilderton and Torgrimsson for the vacuum polarisation…
We study conformations of the Gaussian polymer chains in d-dimensional space in the presence of an external field with the harmonic potential. We apply a path integral approach to derive an explicit expression for the probability…
We analyze the worldline formalism in the presence of a gravitational background. In the worldline formalism a path integral is used to quantize the worldline coordinates of the particles. Contrary to the simpler cases of scalar and vector…
A form of the constraints, specifying a $D$-dimensional manifold embedded in $D+1$ dimensional Euclidean space, is discussed in the path integral formula given by a time discretization. Although the mid-point prescription is privileged in…
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…
We consider two-dimensional quantum gravity coupled to matter in the temporal gauge, using the Polyakov path integral. We show that the integration over the metric can be explicitly performed under some plausible assumptions. We also…
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We present a new method for the consistent construction of time-continuous coherent-state path integrals using the theory of half-form quantization. Through the inversion of the quantization procedure we construct a de-quantization map…