Related papers: Cost of holographic path integrals
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
The path integral for higher-derivative quantum gravity with torsion is considered. Applying the methods of two-dimensional quantum gravity, this path integral is analyzed in the limit of conformally self-dual metrics. A scaling law for…
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
We propose a new method to compute nonlinear transport coefficients in holography, such as nonlinear DC conductivity and nonlinear friction coefficient. The conventional method can be applied only to the models whose action in the gravity…
A new definition for the path integral is proposed in terms of Finsler geometry. The conventional Feynman's scheme for quantisation by Lagrangian formalism suffers problems due to the lack of geometrical structure of the configuration space…
We outline a general derivation of holographic duality between "TQFT gravity" - the path integral of a 3d TQFT summed over different topologies - and an ensemble of boundary 2d CFTs. The key idea is to place the boundary ensemble on a…
We develop a path integrals approach for analyzing stationary light propagation appropriate for photonic crystals. The hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle…
In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and…
In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
Based on the Lewkowycz-Maldacena prescription and the fine structure analysis of holographic entanglement proposed in arXiv:1803.05552, we explicitly calculate the holographic entanglement entropy for warped CFT that duals to AdS$_3$ with a…
Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a…
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…
The costs incurred in a mobile robot (MR) change due to change in physical and environmental factors. Usually, there are two approaches to consider these costs, either explicitly modelling these different factors to calculate the cost or…
Safe path planning is a crucial component in autonomous robotics. The many approaches to find a collision free path can be categorically divided into trajectory optimisers and sampling-based methods. When planning using occupancy maps, the…
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…
Nielsen's geometric approach to quantum circuit complexity provides a Riemannian framework for quantifying the cost of implementing unitary (closed--system) dynamics. For open dynamics, however, the reduced evolution is described by quantum…
The cost functions considered are $c(x,y)=h(x-y)$, where $h\in C^2(\mathbb{R}^n)$, homogeneous of degree $p\geq 2$, with a positive definite Hessian in the unit sphere. We study multivalued monotone maps with respect to that cost and…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…