Least-action principle and path-integral for classical mechanics

Cattaruzza, E.; Gozzi, E.; Neto, Antônio Francisco

doi:10.1103/physrevd.87.067501

Cited by 6 publications

(12 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A quick check of the symmetries, especially the ghost number makes it clear that we are talking about an N T = 2 multiplet as discussed in the text. The occurrence of this topological symmetry algebra has been noted in the literature [68,69]. These references were interested in providing a path integral formulation of classical mechanics as a counterpart to the operator formalism developed by Koopman and von Neumann [70,71].…”

Section: Stochastic Dynamicsmentioning

confidence: 95%

Schwinger-Keldysh formalism. Part I: BRST symmetries and superspace

Haehl

Loganayagam

Rangamani

2017

J. High Energ. Phys.

206

View full text Add to dashboard Cite

Abstract:We review the Schwinger-Keldysh, or in-in, formalism for studying quantum dynamics of systems out-of-equilibrium. The main motivation is to rephrase well known facts in the subject in a mathematically elegant setting, by exhibiting a set of BRST symmetries inherent in the construction. We show how these fundamental symmetries can be made manifest by working in a superspace formalism. We argue that this rephrasing is extremely efficacious in understanding low energy dynamics following the usual renormalization group approach, for the BRST symmetries are robust under integrating out degrees of freedom. In addition we discuss potential generalizations of the formalism that allow us to compute out-of-time-order correlation functions that have been the focus of recent attention in the context of chaos and scrambling. We also outline a set of problems ranging from stochastic dynamics, hydrodynamics, dynamics of entanglement in QFTs, and the physics of black holes and cosmology, where we believe this framework could play a crucial role in demystifying various confusions. Our companion paper [1] describes in greater detail the mathematical framework embodying the topological symmetries we uncover here.

show abstract

Section: Stochastic Dynamicsmentioning

confidence: 95%

Schwinger-Keldysh formalism. Part I: BRST symmetries and superspace

Haehl

Loganayagam

Rangamani

2017

J. High Energ. Phys.

206

View full text Add to dashboard Cite

show abstract

“…We said before that we can realize theλ a as a derivative operator (like in Eq. (13) and obviously the ϕ a as a multiplicative one:φ a |ϕ = ϕ a |ϕ .…”

Section: The Evolution Of ψ(Q P) Is Given By the Liouville Equationmentioning

confidence: 99%

On the metric structure of time in classical and quantum mechanics

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Simulation model of a cubic lattice consists of the parameter points x = d (n 0 , n 1 , n 2 , n 3 ) where d is the lattice spacing and n 1 , n 2 , n 3 are reciprocical lattice vectors where n 0 is redundant parameter. Numerical simulation of channeled ion trajectories coherent in spacetime with a lattice, is performed applying the path integral formalism [18,19] across a system ((1 1 0) Si crystal plane) whose degrees of freedom are related to effective potential field variable / x at each lattice site x. In order to immerse into the simulation model the effective potential induced by the planar channeling oscillations, we applied the prescription for the path integral in the momentum space where particle's Hamiltonian is H = p(t) 2 / 2m + 1/2mx 2 q 2 , (p, q e R 3 ) and p(t) 2 = P j p j (t) 2 ; incorporating the particle dynamics into the former Hamiltonian while summing over all possible paths and integrating over all possible momenta within specified time interval gives where U pl (p(t)) is the total potential in momentum space, which is experienced by the particle as a sum of the potentials of all the planes:…”

Section: Simulation Modelmentioning

confidence: 99%