相关论文: Constructive Representation Theory for the Feynman…

The building blocks of Hudson-Parthasarathy quantum stochastic calculus start with Weyl operators on a symmetric Fock space. To realize a relativistically covariant version of the calculus we construct representations of Poincare group in…

The proper time path integral representation is derived explicitly for Green's functions in QCD. After an introductory analysis of perturbative properties, the total gluonic field is separated in a rigorous way into a nonperturbative…

The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different…

This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a…

We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is…

In this paper an analytic operator-valued generalized Feynman integral was studied on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ is a function space which is induced by the generalized Brownian…

A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical…

In the context of the imaginary-time formalism for a scalar thermal field theory, it is shown that the result of performing the sums over Matsubara frequencies associated with loop Feynman diagrams can be written, for some classes of…

A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative…

The work fluctuation theorem (FT) is a symmetry connecting the moment generating functions (MGFs) of the work extracted in a given process and in its time-reversed counterpart. We show that, equivalently, the FT for work in isolated quantum…

We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…

Scalar field theories with quartic interactions are of central interest in the study of second-order phase transitions. For three-dimensional theories, numerous studies make use of the fixed-dimensional perturbative computation of [B.…

An abstract formulation of quantum dynamics in the presence of a general set of quantum constraints is developed. Our constructive procedure is such that the relevant projection operator onto the physical Hilbert space is obtained with a…

We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master…

Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…

We first formulate a definition of tensor product for two modules for a vertex operator algebra in terms of a certain universal property and then we give a construction of tensor products. We prove the unital property of the adjoint module…

A modification of the Fokker action is proposed, which allows one to formulate the covariant quantum theory of the charge system, in which the proper time of each particle serves as the evolution parameter and the particles themselves…

Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view.…

We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…

Feynman proposed a postulate or a method of quantization in his celebrated paper in 1948. Applying Feynman's postulate to temporally continuous quantum measurements of the positions of particles, Mensky proposed the restricted Feynman path…