Related papers: A Consistent Path Integral Approach to Higher Deri…
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to…
The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known…
Introducing a perturbative definition, phase space path integrals can be calculated without slicing. This leads to a short-time expansion of the quantum-mechanical path amplitude, or a high-temperature expansion of the unnormalized density…
We analyze the quantization of the Pais-Uhlenbeck fourth order oscillator within the framework of deformation quantization. Our approach exploit the Noether symmetries of the system by proposing integrals of motion as the variables to…
We provide a new canonical approach for studying the quantum mechanical damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the elementary modes of the problem,…
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…
Quantum field theory in curved spacetimes suffers in general from an infinite ambiguity in the choice of Fock representation and associated vacuum. In cosmological backgrounds, the requirement of a unitary implementation of the field…
It is shown that the introduction of an upper limit to the proper acceleration of a particle can smooth the problem of ultraviolet divergencies in local quantum field theory. For this aim, the classical model of a relativistic particle with…
Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to…
We give two novel proofs that the path integral and stochastic quantizations of generic scalar Euclidean quantum field theories are equivalent. Our proofs rely on Taylor interpolations indexed by forests, in the fashion of constructive…
A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic…
The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. Firstly, we review the five-dimensional approach to…
We extend, to the quantum domain, the results obtained in [Nucl. Phys. B 885 (2014) 150] and [Phys. Lett. B 738 (2014) 405] concerning the Niederer's transformation for the Pais-Uhlenbeck oscillator. Namely, the quantum counterpart (an…
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…
Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…
We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White…
Studying phase transitions in interacting quantum field theories generally requires the numerical study of the dynamical system on an N-dimensional lattice, which is, in most cases, computationally quite the challenging task even with…
Krein-de Branges spectral theory establishes a correspondence between the class of differential operators called canonical Hamiltonian systems and measures on the real line with finite Poisson integral. We further develop this area by…
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to…