Related papers: Real-Time Feynman Path Integral Realization of Ins…
Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time…
We define the idea of {\it real path quantum theory}, a realist generalisation of quantum theory in which it is postulated that the configuration space path actually followed by a closed quantum system is probabilistically chosen. This is…
In this lecture a short introduction is given into the theory of the Feynman path integral in quantum mechanics. The general formulation in Riemann spaces will be given based on the Weyl- ordering prescription, respectively product ordering…
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…
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…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with…
Feynman proposed a postulate or a method of quantization in his celebrated paper in 1948. Applying Feynman's postulate to temporally continuous quantum measurements of the positions of particles, Mensky proposed the restricted Feynman path…
We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with renormalized parameters. We present numerical results for the $V \sim x^{4}$ potential. The renormalized action…
An instanton method is proposed to investigate the quantum tunneling between two weakly-linked Bose-Einstein condensates confined in double-well potential traps. We point out some intrinsic pathologies in the earlier treatments of other…
The imaginary part of the one loop effective action in external backgrounds can be efficiently computed using worldline instantons which are closed periodic paths in spacetime. Exact solutions for nonstatic backgrounds are only known in…
We consider quantum tunnelling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. We derive a generalization of instanton theory for these asymmetric…
High precision calculations in perturbative QFT often require evaluation of big collection of Feynman integrals. Complexity of this task can be greatly reduced via the usage of linear identities among Feynman integrals. Based on…
Quantum tunneling from a thin wire or a thin film through a static potential barrier in a zero magnetic field is studied. The wire or the film should satisfy a condition of transverse quantization of levels and be inhomogeneous. Depending…
Quantum tunneling through an almost classical potential barrier can be strongly enhanced by a nonstationary field so that the penetration through the barrier becomes not exponentially small. This constitutes an extremely unusual phenomenon…
We derive the path-integral representation of the fractional Ornstein-Uhlenbeck process driven by Riemann-Liouville fractional Gaussian noise, for both the subdiffusive and superdiffusive regimes. We express the corresponding action, which…
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…
Behavior of the Euclidean path integral at large orders of the perturbation series is studied. When the model allows tunneling, the path-integral functional in the zero instanton sector is known to be dominated by bounce-like configurations…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential…
Semi-classical analysis is used to investigate synchronous quantum tunneling in a multidimensional potential energy surface (PES) characterized by four degenerate minima, serving as a foundational model for coupled vibrational modes. The…