scholarly journals The zeta function method and the harmonic oscillator propagator

2001 ◽  
Vol 69 (2) ◽  
pp. 232-235 ◽  
Author(s):  
F. A. Barone ◽  
C. Farina
Keyword(s):  
Harmonic Oscillator ◽  
Zeta Function ◽  
Function Method

Renormalization In Quantum Gauge Theory Using Zeta-Function Method

2009 ◽  
Author(s):  
Viorel Chiritoiu ◽  
Gheorghe Zet ◽  
Madalin Bunoiu ◽  
Iosif Malaescu
Keyword(s):  
Gauge Theory ◽  
Zeta Function ◽  
Function Method ◽  
Quantum Gauge Theory

scholarly journals Testing the surrogate zeta-function method

1986 ◽  
Vol 64 (5) ◽  
pp. 633-636 ◽  
Author(s):  
Alan Chodos ◽  
Eric Myers
Keyword(s):  
Euclidean Space ◽  
Zeta Function ◽  
Minkowski Space ◽  
Function Method ◽  
Casimir Energy ◽  
Kaluza Klein

Use of the surrogate zeta-function method was crucial in calculating the Casimir energy in non-Abelian Kaluza–Klein theories. We establish the validity of this method for the case where the background metric is (Euclidean space) × (N sphere). Our techniques do not apply to the case where the background is (Minkowski space) × (N sphere).

The Riemann Zeta Function and the Inverted Harmonic Oscillator

1997 ◽  
Vol 254 (1) ◽  
pp. 25-40 ◽  
Author(s):  
R.K. Bhaduri ◽  
Avinash Khare ◽  
S.M. Reimann ◽  
E.L. Tomusiak
Keyword(s):  
Harmonic Oscillator ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Thermal Properties of the One-Dimensional Duffin–Kemmer–Petiau Oscillator Using Hurwitz Zeta Function

2015 ◽  
Vol 70 (10) ◽  
pp. 867-874 ◽  
Author(s):  
Abdelamelk Boumali
Keyword(s):  
Free Energy ◽  
Thermal Properties ◽  
Zeta Function ◽  
Function Method ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Hurwitz Zeta Function ◽  
Expectation Value ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we investigated the thermodynamics properties of the one-dimensional Duffin–Kemmer–Petiau oscillator by using the Hurwitz zeta function method. In particular, we calculated the following main thermal quantities: the free energy, the total energy, the entropy, and the specific heat. The Hurwitz zeta function allowed us to compute the vacuum expectation value of the energy of our oscillator.

scholarly journals V-Function Method: Some Solutions of Direct and Inverse Dynamics Problems in A New Statement

2019 ◽  
Vol 56 (1) ◽  
pp. 70-81 ◽  
Author(s):  
Nail T. Valishin ◽  
Fan T. Valishin
Keyword(s):  
Harmonic Oscillator ◽  
Function Method ◽  
Wave Motion ◽  
Inverse Dynamics ◽  
Local Variation ◽  
Object Motion ◽  
Uniform Motion ◽  
Mechanical Analogy ◽  
Wave Nature ◽  
Dynamics Problems

Abstract Based on the V-function method, the properties of wave nature of object motion are studied for object uniform motion with constant speed and for harmonic oscillator. It follows from the V-function method that object wave motion is inseparably linked with its trajectory motion. The V-function method consists of the principle of local variation and a new statement of the direct and inverse dynamics problems. The proposed approach made it possible to make the optico-mechanical analogy that obtained a new continuation. A comparison is made with the results obtained by Schrödinger for a harmonic oscillator.

scholarly journals Equivalence of zeta function technique and Abel–Plana formula in regularizing the Casimir energy of hyper-rectangular cavities

2014 ◽  
Vol 29 (35) ◽  
pp. 1450181
Author(s):  
Rui-Hui Lin ◽  
Xiang-Hua Zhai
Keyword(s):  
Zeta Function ◽  
Regularization Method ◽  
Function Method ◽  
Casimir Energy ◽  
Function Technique ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Epstein Zeta Function ◽  
Formula Method ◽  
Reflection Formula

Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic continuation. By contrast, Abel–Plana formula method permits explicit separation of divergent terms. In regularizing the Casimir energy for a massless scalar field in a D-dimensional rectangular box, we give the rigorous proof of the equivalence of the two methods by deriving the reflection formula of Epstein zeta function from repeatedly application of Abel–Plana formula and giving the physical interpretation of the infinite integrals. Our study may help with the confidence of choosing any regularization method at convenience among the frequently used ones, especially the zeta function method, without the doubts of physical meanings or mathematical consistency.

scholarly journals Regularization, zeta function method

2004 ◽  
pp. 345-345
Author(s):  
Wit de Bernard ◽  
Proeyen Van Antoine ◽  
Majid Shahn ◽  
Reinhard Oehme ◽  
Duplij Steven ◽  
...  
Keyword(s):  
Zeta Function ◽  
Function Method

scholarly journals The quantum geometric tensor from generating functions

2019 ◽  
Vol 17 (02) ◽  
pp. 1950017 ◽  
Author(s):  
Javier Alvarez-Jimenez ◽  
J. David Vergara
Keyword(s):  
Quantum Information ◽  
Harmonic Oscillator ◽  
Generating Function ◽  
Generating Functions ◽  
Function Method ◽  
New Method ◽  
Berry Curvature ◽  
Information Metric

We introduce a new method to compute the Quantum Geometric Tensor, this procedure allows us to compute the Quantum Information Metric and the Berry curvature perturbatively for a theory with an arbitrary interaction Hamiltonian. The calculation uses the generating function method, and it is illustrated with the harmonic oscillator with a linear and a quartic perturbation.

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