Related papers: Path integral for quantum Mabuchi K-energy
A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
We use the geometry of the space of fields for gauged supersymmetric mechanics to construct the twisted differential equivariant K-theory of a manifold with an action by a finite group.
I assume a universe whereby the speed of light and the planck constant are not constants but instead parameters that vary locally in time-and space. When describing motion, I am able to derive a modified path integral description at the…
Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
In this letter, we introduce Geometric Model Predictive Path Integral (GMPPI), a sampling-based controller capable of tracking agile trajectories while avoiding obstacles. In each iteration, GMPPI generates a large number of candidate…
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…
I review the generating function for quantum-statistical mechanics, known as the Feynman-Vernon influence functional, the decoherence functional, or the Schwinger-Keldysh path integral. I describe a probability-conserving $i\varepsilon$…
Using a gauge covariant operator technique we deduce the path integral for a charged particle in a stationary magnetic field, verifying the "midpoint rule" for the discrete form of the interaction term with the vector potential.
For description of the quantum dynamics on a curved group manifold the path integrals in a space of the group parameters is offered. The formalism is illustrated by the $H$-atom problem.
Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…
The formulation of the relativistic spinless path integral on the general affine space is presented. For the one dimensional space, the Duru-Kleinert (DK) method and the $\delta $-function perturbation technique are applied to solve the…
Classical methods of differential geometry are used to construct equations of motion for particles in quantum, electrodynamic and gravitational fields. For a five dimensional geometrical system, the equivalence principle can be extended.…
A theorem that constructs a path integral solution for general second order partial differential equations is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial…
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…
We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x2013}$ in particular, the coherent state path integral. We…
A new routine is proposed to relate Loop Quant Cosmology (LQC) to Loop Quantum Gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical…
Using the path integral measure factorization method based on the nonlinear filtering equation from the stochastic process theory, we consider the reduction procedure in Wiener path integrals for a mechanical system with symmetry that…
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a…