Related papers: Constructive Representation Theory for the Feynman…
The equivalence of two formulations of Fokker's quantum theory is proved - based on the Feynman functional integral representation of the propagator for a system of charges with direct electromagnetic interaction and the quantum principle…
A kink-based expression for the canonical partition function is developed using Feynman's path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on…
The perturbative framework of the space-time non-commutative real scalar field theory is formulated, based on the unitary S-matrix. Unitarity of the S-matrix is explicitly checked order by order using the Heisenberg picture of Lagrangian…
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…
In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…
The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over…
The unmodified Heisenberg-Pauli canonical formalism of quantum field theory applied to a self-interacting scalar boson field is shown to make sense mathematically in a framework of generalized functions adapted to nonlinear operations. The…
We give a unitary irreducible representation of the proper Poincar\'e group that leads to an operational version of the classical relativistic dynamics of a massive spinless particle. Unlike quantum mechanics, in this operational theory…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation…
Approximation theory is a substantial field of mathematical analysis that emerged in the 19th century and has been developed by mathematicians across the globe ever since. Its importance has increased over time, as it provides solutions to…
A new representation -which is similar to the Bargmann representation- of the creation and annihilation operators is introduced, in which the operators act like "multiplication with" and like "derivation with respect to" a single real…
In this work, we investigate a very important but unstressed result in the work of Carl M. Bender, Jun-Hua Chen, and Kimball A. Milton ( J.Phys.A39:1657-1668, 2006). In this article, Bender \textit{et.al} have calculated the vacuum energy…
We sketch a Weyl creation operator approach to the Riemann Hypothesis; i.e.,arithmetic on the Weyl algebras with ergodic theory to transport operators. We prove that finite Hasse-Dirichlet alternating zeta functions or eta functions can be…
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams…
A general formlulation for discrete-time quantum mechanics, based on Feynman's method in ordinary quantum mechanics, is presented. It is shown that the ambiguities present in ordinary quantum mechanics (due to noncommutativity of the…
We study pure noncommutative U(1) gauge theory representing its one-loop effective action in terms of a phase space worldline path integral. We write the quadratic action using the background field method to keep explicit gauge invariance,…
In the first part of our paper we analyze bisolutions and inverses of (non-autonomous) evolution equations. We are mostly interested in pseudo-unitary evolutions on Krein spaces, which naturally arise in linear Quantum Field Theory. We…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The…