Related papers: Functional integral for non-Lagrangian systems
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
Response functions are key observables for probing the structure and dynamics of many-body systems. We introduce and demonstrate a quantum-classical framework for computing response functions of general many-fermion systems that also…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
The fractional quantum and statistical mechanics have been developed via new path integrals approach.
We formalize Feynman's construction of the quantum mechanical path integral. To do this, we shift the emphasis in differential geometry from the tangent bundle onto the pair groupoid. This allows us to use the van Est map and the piecewise…
There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang-Mills fields, and fermions. The…
Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…
We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the…
We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…
We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for…
Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and highlights the role of the Lagrangian phase…
We study the Caldeira-Leggett model where a quantum Brownian particle interacts with an environment or a bath consisting of a collection of harmonic oscillators in the path integral formalism. Compared to the contours that the paths take in…
Standard derivations of the functional integral in non-equilibrium quantum field theory are based on the discrete time representation. In this work we derive the non-equilibrium functional integral for non-interacting bosons and fermions…
We consider the quantum mechanical analog of the nonlinear sigma model. There are difficulties to completely embed this theory by directly using the Batalin, Fradkin, Fradkina, and Tyutin (BFFT) formalism. We show in this paper how the BFFT…
We present a string theory realization for the correspondence between quantum integrable models and supersymmetric gauge theories. The quantization results from summing the effects of fundamental strings winding around a compact direction.…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…
Hamiltonian Mechanics works for conserved systems and Quantum Mechanics is given in Hamiltonian language. It is considered that complexifying the quantum Hamiltonian, a balanced loss and gain model can be created. The usual mathematics of…
It is possible to introduce external time dependent back ground fields in the formulation of a system as fields whose dynamics can not be deduced from Euler Lagrange equations of motion. This method leads to singular Lagrangians for real…