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.

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.

scholarly journals Functional integrals method for systems of stochastic differential equations

2018 ◽  
Vol 54 (3) ◽  
pp. 279-289 ◽  
Author(s):  
E. A. Ayryan ◽  
A. D. Egorov ◽  
D. S. Kulyabov ◽  
V. B. Malyutin ◽  
L. A. Sevastyanov
Keyword(s):  
Riemannian Manifold ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lagrange Equation ◽  
Classical Trajectory ◽  
Functional Integral ◽  
Diffusion Matrix ◽  
Approximate Evaluation ◽  
Functional Integrals ◽  
Zero Curvature

Systems of stochastic differential equations, for which the Riemannian manifold generated by a diffusion matrix has zero curvature, are considered in this article. The method for approximate evaluation of characteristics of the solution of the systems of stochastic differential equations is proposed. This method is based on the representation of the probability density function through the functional integral. To compute functional integrals we use the expansion of action with respect to a classical trajectory, for which the action takes an extreme value. The classical trajectory is found as the solution of the multidimensional Euler – Lagrange equation.

scholarly journals Semiclassical approximation of functional integrals

2020 ◽  
Vol 56 (2) ◽  
pp. 166-174
Author(s):  
V. B. Malyutin ◽  
B. O. Nurjanov
Keyword(s):  
Numerical Analysis ◽  
Calculation Method ◽  
Semiclassical Approximation ◽  
Classical Trajectory ◽  
Functional Integral ◽  
The Other ◽  
Planck Constant ◽  
Functional Integrals ◽  
Expansion In Eigenfunctions ◽  
Comparison Of The Results

In this paper, we consider a semiclassical approximation of special functional integrals with respect to the conditional Wiener measure. In this apptoximation we use the expansion of the action with respect to the classical trajectory. In so doing, the first three terms of expansion are taken into account. Semiclassical approximation may be interpreted as an expansion in powers of the Planck constant. The novelty of this work is the numerical analysis of the accuracy of the semiclassical approximation of functional integrals. A comparison of the results is used for numerical analysis. Some results are obtained by means of semiclassical approximation, while the other by means of the functional integrals calculation method based on the expansion in eigenfunctions of the Hamiltonian generating a functional integral.

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.

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.

scholarly journals Approximate evaluation of the functional integrals generated by the Dirac equation with pseudospin symmetry

2021 ◽  
Vol 57 (1) ◽  
pp. 14-22
Author(s):  
Е. A. Ayryan ◽  
М. Hnatic ◽  
V. В. Malyutin
Keyword(s):  
Dirac Equation ◽  
Evolution Operator ◽  
Type Equation ◽  
Pseudospin Symmetry ◽  
Functional Integral ◽  
Eigenvalues And Eigenfunctions ◽  
Functional Integrals ◽  
Vector Potentials ◽  
The Matrix ◽  
Sequence Method

 In this paper, the matrix-valued functional integrals generated by the Dirac equation with relativistic Hamiltonian are considered. The Dirac Hamiltonian contains scalar and vector potentials. The sum of the scalar and vector potentials is equal to zero, i.e., the case of pseudospin symmetry is investigated. In this case, a Schrödinger-type equation for the eigenvalues and eigenfunctions of the relativistic Hamiltonian generating the functional integral is constructed. The eigenvalues and eigenfunctions of the Schrödinger-type operator are found using the Sturm sequence method and the reverse iteration method. A method for the evaluation of matrix-valued functional integrals is proposed. This method is based on the relation between the functional integral and the kernel of the evolution operator with the relativistic Hamiltonian and the expansion of the kernel of the evolution operator in terms of the found eigenfunctions of the relativistic Hamiltonian. 

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.

Efficient Electromagnetic Analysis of a Dispersive Head Model Due to Smart Glasses Embedded Antennas at Wi-Fi and 5G Frequencies

2021 ◽  
Vol 36 (2) ◽  
pp. 159-167
Author(s):  
Fatih Kaburcuk ◽  
Atef Elsherbeni
Keyword(s):  
Numerical Study ◽  
Computation Time ◽  
Human Head ◽  
Head Model ◽  
Computer Memory ◽  
Large Computer ◽  
Smart Glasses ◽  
Embedded Antennas ◽  
Human Head Model ◽  
Difference Time

Numerical study of electromagnetic interaction between an adjacent antenna and a human head model requires long computation time and large computer memory. In this paper, two speeding up techniques for a dispersive algorithm based on finite-difference time-domain method are used to reduce the required computation time and computer memory. In order to evaluate the validity of these two speeding up techniques, specific absorption rate (SAR) and temperature rise distributions in a dispersive human head model due to radiation from an antenna integrated into a pair of smart glasses are investigated. The antenna integrated into the pair of smart glasses have wireless connectivity at 2.4 GHz and 5th generation (5G) cellular connectivity at 4.9 GHz. Two different positions for the antenna integrated into the frame are considered in this investigation. These techniques provide remarkable reduction in computation time and computer memory.

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.

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