Path integral treatment for the one‐dimensional Natanzon potentials

1993 ◽  
Vol 34 (4) ◽  
pp. 1257-1269 ◽  
Author(s):  
L. Chetouani ◽  
L. Guechi ◽  
A. Lecheheb ◽  
T. F. Hammann
Keyword(s):  
Path Integral ◽  
One Dimensional ◽  
Integral Treatment ◽  
The One

scholarly journals Path-integral approach to the one-dimensional large-UHubbard model

1992 ◽  
Vol 45 (14) ◽  
pp. 7850-7871 ◽  
Author(s):  
Z. Y. Weng ◽  
D. N. Sheng ◽  
C. S. Ting ◽  
Z. B. Su
Keyword(s):  
Path Integral ◽  
Integral Approach ◽  
One Dimensional ◽  
Path Integral Approach ◽  
The One

Dirac oscillator in a uniform electric field: Path integral treatment

2019 ◽  
Vol 34 (30) ◽  
pp. 1950246
Author(s):  
Hassene Bada ◽  
Mekki Aouachria
Keyword(s):  
Energy Spectrum ◽  
Electric Field ◽  
Path Integral ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Fermionic Model ◽  
Internal Motions ◽  
Integral Treatment ◽  
The One

In this paper, the propagator of a two-dimensional Dirac oscillator in the presence of a uniform electric field is derived by using the path integral technique. The fact that the globally named approach is used in this work redirects, beforehand, our search for the propagator of the Dirac equation to that of the propagator of its quadratic form. The internal motions relative to the spin are represented by two fermionic oscillators, which are described by Grassmannian variables, according to Schwinger’s fermionic model. Once the integration over the anticommuting variables (Grassmannian variables) is accomplished, the problem becomes the one of finding a non-relativistic propagator with only bosonic variables. The energy spectrum of the electron and the corresponding eigenspinors are also obtained in this work.

scholarly journals Comments on open string with ‘massive’ boundary term

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190748
Author(s):  
Arkady A. Tseytlin
Keyword(s):  
Scattering Amplitudes ◽  
Partition Function ◽  
Gauge Field ◽  
Path Integral ◽  
Open String ◽  
One Dimensional ◽  
Conformally Invariant ◽  
Additional Constant ◽  
The One ◽  
Definition Of

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

scholarly journals A COHERENT STATE PATH INTEGRAL FOR ANYONS

1995 ◽  
Vol 10 (12) ◽  
pp. 985-989 ◽  
Author(s):  
J. GRUNDBERG ◽  
T.H. HANSSON
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Change Of Variables ◽  
The One ◽  
State Path

We derive an su (1, 1) coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to an su (1, 1) version of the Holstein-Primakoff transformation.

Thermal Vacuum Polarization Using the Quantum Mechanical Path Integral

1997 ◽  
Vol 12 (30) ◽  
pp. 5387-5396 ◽  
Author(s):  
D. G. C. Mckeon
Keyword(s):  
Path Integral ◽  
Vacuum Polarization ◽  
Thermal Field ◽  
Quantum Mechanical ◽  
Loop Order ◽  
Thermal Vacuum ◽  
One Dimensional ◽  
Loop Expansion ◽  
High Temperature Expansion ◽  
The One

It has been shown how the quantum mechanical path integral can be used to do perturbative calculations in both quantum and thermal field theory to any order of the loop expansion. However, it is not readily apparent how gauge invariance is made manifest in this approach; in this paper we demonstrate how the vacuum polarization in electrodynamics at one-loop order is in fact transverse. We employ the one-dimensional Green's function [Formula: see text] in conjunction with an integration-by-parts procedure akin to that used by Strassler and Bern and Kosower. Surface terms in this approach are all zero. We obtain the high temperature expansion for the vacuum polarization in the static limit.

scholarly journals A PATH INTEGRAL APPROACH TO DERIVATIVE SECURITY PRICING I: FORMALISM AND ANALYTICAL RESULTS

1999 ◽  
Vol 02 (04) ◽  
pp. 381-407 ◽  
Author(s):  
ELEONORA BENNATI ◽  
MARCO ROSA-CLOT ◽  
STEFANO TADDEI
Keyword(s):  
Financial Markets ◽  
Path Integral ◽  
Integral Approach ◽  
Covariant Formulation ◽  
One Dimensional ◽  
Path Integral Approach ◽  
Financial Interest ◽  
Security Pricing ◽  
The One ◽  
Pde Methods

We use a path integral approach for solving the stochastic equations underlying the financial markets, and show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the multi-dimensional cases, with point dependent drift and volatility, and describe a covariant formulation which allows general changes of variables. Finally we apply the method to some economic models with analytical solutions. In particular, we evaluate the expectation value of functionals which correspond to quantities of financial interest.

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