The Euclidean Functional Integrals

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Perturbation Theory ◽  
Euclidean Space ◽  
Functional Integral ◽  
Wick Rotation ◽  
Functional Integrals ◽  
Feynman Rules

The Wick rotation and the functional integral in Euclidean space. Some mathematical theorems. Perturbation theory and Feynman rules in Euclidean space.

scholarly journals Approximate evaluation of functional integrals generated by the relativistic Hamiltonian

2020 ◽  
Vol 56 (1) ◽  
pp. 72-83
Author(s):  
E. A. Ayryan ◽  
M. Hnatic ◽  
V. B. Malyutin
Keyword(s):  
Perturbation Theory ◽  
Computation Time ◽  
Functional Integral ◽  
The Other ◽  
Computer Memory ◽  
Approximate Evaluation ◽  
Functional Integrals ◽  
Small Correction ◽  
Sequence Method ◽  
Method Of Evaluation

An approximate evaluation of matrix-valued functional integrals generated by the relativistic Hamiltonian is considered. The method of evaluation of functional integrals is based on the expansion in the eigenfunctions of Hamiltonian generating the functional integral. To find the eigenfunctions and the eigenvalues the initial Hamiltonian is considered as a sum of the unperturbed operator and a small correction to it, and the perturbation theory is used. The eigenvalues and the eigenfunctions of the unperturbed operator are found using the Sturm sequence method and the reverse iteration method. This approach allows one to significantly reduce the computation time and the used computer memory compared to the other known methods.

NEW PERTURBATION THEORY FOR QUANTUM FIELD THEORY: CONVERGENT SERIES INSTEAD OF ASYMPTOTIC EXPANSIONS

1995 ◽  
Vol 10 (39) ◽  
pp. 3033-3041 ◽  
Author(s):  
V.V. BELOKUROV ◽  
E.T. SHAVGULIDZE ◽  
YU. P. SOLOVYOV
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Expansions ◽  
Quantum Physics ◽  
Functional Integration ◽  
Convergent Series ◽  
Functional Integral ◽  
Quantum Field ◽  
Coupling Constant ◽  
Functional Integrals ◽  
New Perturbation

Asymptotic expansions, employed in quantum physics as series of perturbation theory, appear as a result of the representation of functional integrals by power series with respect to coupling constant. To derive these series one has to change the order of functional integration and infinite summation. In general, this procedure is incorrect and is responsible for the divergence of the asymptotic expansions. In the present work, we suggest a method of construction of a new perturbation theory. In the framework of this perturbation theory, a convergent series corresponds to any physical quantity represented by a functional integral. The relations between the coefficients of these series and those of the asymptotic expansions are established.

THE FUNCTIONAL INTEGRAL ON THE HALF-LINE

1990 ◽  
Vol 05 (15) ◽  
pp. 3029-3051 ◽  
Author(s):  
EDWARD FARHI ◽  
SAM GUTMANN
Keyword(s):  
Time Evolution ◽  
Wide Class ◽  
Green's Functions ◽  
Green’S Functions ◽  
Functional Integral ◽  
Half Line ◽  
Functional Integrals ◽  
Quantum Hamiltonian ◽  
Do So

A quantum Hamiltonian, defined on the half-line, will typically not lead to unitary time evolution unless the domain of the Hamiltonian is carefully specified. Different choices of the domain result in different Green’s functions. For a wide class of non-relativistic Hamiltonians we show how to define the functional integral on the half-line in a way which matches the various Green’s functions. To do so we analytically continue, in time, functional integrals constructed with real measures that give weight to paths on the half-line according to how much time they spend near the origin.

scholarly journals Some comments on infinities on quantum field theory: A functional integral approach

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Luiz C. L. Botelho
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Function Space ◽  
Functional Integral ◽  
Field Theories ◽  
Integral Approach ◽  
Quantum Field ◽  
Functional Integrals ◽  
Euclidean Field ◽  
The Subject

AbstractWe analyze on the formalism of probabilities measures-functional integrals on function space the problem of infinities on Euclidean field theories. We also clarify and generalize our previous published studies on the subject.

scholarly journals Hamiltonian approach to QCD in Coulomb gauge: Perturbative treatment of the quark sector

2015 ◽  
Vol 30 (17) ◽  
pp. 1550100 ◽  
Author(s):  
Davide R. Campagnari ◽  
Hugo Reinhardt
Keyword(s):  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Quark Propagator ◽  
Functional Integral ◽  
Coulomb Gauge ◽  
Hamiltonian Approach ◽  
Equal Time ◽  
Quark Sector ◽  
Schrödinger Perturbation ◽  
Perturbative Treatment

We study the static gluon and quark propagator of the Hamiltonian approach to quantum chromodynamics in Coulomb gauge in one-loop Rayleigh–Schrödinger perturbation theory. We show that the results agree with the equal-time limit of the four-dimensional propagators evaluated in the functional integral (Lagrangian) approach.

Perturbation Theory with Convergent Series for Arbitrary Values of Coupling Constant

1997 ◽  
Vol 12 (10) ◽  
pp. 661-672 ◽  
Author(s):  
V. V. Belokurov ◽  
V. V. Kamchatny ◽  
E. T. Shavgulidze ◽  
Yu. P. Solovyov
Keyword(s):  
Perturbation Theory ◽  
Regularization Parameter ◽  
Convergent Series ◽  
Coupling Constants ◽  
Coupling Constant ◽  
Functional Integrals

In this letter, the method of the approximative calculation of functional integrals with any given accuracy1,2 is developed. Here we use the independence of the integrals on an auxiliary regularization parameter to simplify the calculations. Also we propose a modification of the method that proves to be more convenient for calculations with large values of coupling constants.

scholarly journals Approximate evaluation of functional integrals with centrifugal potential

2019 ◽  
Vol 55 (2) ◽  
pp. 152-157 ◽  
Author(s):  
V. B. Malyutin
Keyword(s):  
Eigenvalue Problem ◽  
Centrifugal Force ◽  
Computation Time ◽  
Functional Integral ◽  
Computer Memory ◽  
Approximate Evaluation ◽  
Functional Integrals ◽  
Sequence Method

Approximate evaluation of functional integrals containing a centrifugal potential is considered. By a centrifugal potential is understood a potential arising from a centrifugal force. A combination of the method based on expanding into a series of the eigenfunctions of a Hamiltonian generating a functional integral and the Sturm sequence method for the eigenvalue problem is used for approximate evaluation of functional integrals. This combination allows one to significantly reduce a computation time and a used computer memory volume in comparison to other known methods.

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