Related papers: New Dirac Delta function based methods with applic…
We study perturbation theory in certain quantum mechanics problems in which the perturbing potential diverges at some points, even though the energy eigenvalues are smooth functions of the coefficient of the potential. We discuss some of…
We apply the linear delta expansion to the quantum mechanical version of the slow rollover transition which is an important feature of inflationary models of the early universe. The method, which goes beyond the Gaussian approximation,…
The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in…
We show how the linear delta expansion, as applied to the slow-roll transition in quantum mechanics, can be recast in the closed time-path formalism. This results in simpler, explicit expressions than were obtained in the Schr\"odinger…
Some quantum mechanical potentials, singular at short distances, lead to ultraviolet divergences when used in perturbation theory. Exactly as in quantum field theories, but much simpler, regularization and renormalization lead to finite…
We analyze a class of coupled quantum systems whose dynamics can be understood via two uncoupled, lower-dimensional quantum settings with auxiliary interactions. The general reduction scheme, based on algebraic properties of the potential…
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
Dynamical mean-field theory (DMFT) is one of the most widely used theoretical methods for electronic structure calculations, providing self-consistent solutions even in low-temperature regimes, which are exact in the limit of infinite…
The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are…
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like…
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically…
We study quantization of a self-interacting scalar field within the unfolded dynamics approach. To this end we find and analyze a classical unfolded system describing 4d off-shell scalar field with a general self-interaction potential. Then…
We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those connected with the magnetic…
We present some exact results about universal quantities derived from the local density matrix, for a free massive Dirac field in two dimensions. We first find the trace of powers of the density matrix in a novel fashion, which involves the…
A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity.…
Correlation functions in one-dimensional complex scalar field theory provide a toy model for phase fluctuations, sign problems, and signal-to-noise problems in lattice field theory. Phase unwrapping techniques from signal processing are…
We show, in great detail, how the perturbative tools of quantum field theory allow one to rigorously obtain: a ``categorified'' Faa di Bruno type formula for multiple composition, an explicit formula for reversion and a proof of…
We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate…