scholarly journals Beyond the Fröhlich Hamiltonian: Path-integral treatment of large polarons in anharmonic solids

2021 ◽  
Vol 103 (18) ◽  
Author(s):  
Matthew Houtput ◽  
Jacques Tempere
Keyword(s):  
Path Integral ◽  
Hamiltonian Path ◽  
Integral Treatment

scholarly journals Finite BRST–anti-BRST transformations in generalized Hamiltonian formalism

2014 ◽  
Vol 29 (27) ◽  
pp. 1450159 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Dynamical Systems ◽  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Constrained Dynamical Systems

We introduce the notion of finite BRST–anti-BRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, both global and field-dependent, with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in the path integral. It turns out that the finite transformations are quadratic in their parameters. Exactly as in the case of finite field-dependent BRST–anti-BRST transformations for the Yang–Mills vacuum functional in the Lagrangian formalism examined in our previous paper [arXiv:1405.0790 [hep-th]], special field-dependent BRST–anti-BRST transformations with functionally-dependent parameters λa= ∫ dt(saΛ), generated by a finite even-valued function Λ(t) and by the anticommuting generators saof BRST–anti-BRST transformations, amount to a precise change of the gauge-fixing function for arbitrary constrained dynamical systems. This proves the independence of the vacuum functional under such transformations. We derive a new form of the Ward identities, depending on the parameters λaand study the problem of gauge dependence. We present the form of transformation parameters which generates a change of the gauge in the Hamiltonian path integral, evaluate it explicitly for connecting two arbitrary Rξ-like gauges in the Yang–Mills theory and establish, after integration over momenta, a coincidence with the Lagrangian path integral [arXiv:1405.0790 [hep-th]], which justifies the unitarity of the S-matrix in the Lagrangian approach.

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.

FORMAL PATH INTEGRAL FOR THEORIES WITH NONCANONICAL COMMUTATION RELATIONS

1989 ◽  
Vol 04 (11) ◽  
pp. 1001-1011 ◽  
Author(s):  
I.A. BATALIN ◽  
E.S. FRADKIN
Keyword(s):  
Path Integral ◽  
Hamiltonian Path ◽  
Generating Functional ◽  
Commutation Relations ◽  
S Matrix ◽  
Formal Level

For theories with noncanonical commutation relations, the generating functional (S-matrix) is constructed at a formal level, as a Hamiltonian path integral.

Path‐integral treatment of multi‐mode vibronic coupling

1994 ◽  
Vol 100 (2) ◽  
pp. 926-937 ◽  
Author(s):  
Stefan Krempl ◽  
Manfred Winterstetter ◽  
Heiko Plöhn ◽  
Wolfgang Domcke
Keyword(s):  
Path Integral ◽  
Vibronic Coupling ◽  
Integral Treatment ◽  
Multi Mode

PATH INTEGRAL ON THE EXTREME FIELD CONFIGURATIONS

2011 ◽  
Vol 26 (01) ◽  
pp. 135-148
Author(s):  
V. M. KHATSYMOVSKY
Keyword(s):  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Tangential Component ◽  
Generalized Function ◽  
Time Axis ◽  
Generalized Coordinates ◽  
Fast Change ◽  
Integral Measure ◽  
Gravity System

The canonical Hamiltonian path integral measure obeys certain rule which relates such measure on the paths defined on the whole time axis to the measures on the paths defined on the regions constituting the time axis. We show that this "gluing" rule can be reproduced without referring to Hamiltonian formalism, by substituting field configurations with arbitrarily fast change of the fields at the boundary points of these regions into action and viewing the path integral in the sense of generalized function. Now the coordinate along which gluing proceeds can be not only the time. The piecewise-flat (simplicial) minisuperspace gravity system is considered. Arbitrarily fast change of the (tangential component of) metric between the two 4-simplices with common 3-face is studied. That is, we generalize piecewise-flat anzats by allowing tangential metric to be function of the distance from the 3-face in the neighborhood of this 3-face. The action is nondegenerate (nonsingular) with respect to these additional generalized coordinates. The rule for gluing the path integral measures on separate 4-simplices is found. The resulting general expression covers a large variety of the measures including those usually used in numerical calculations and allows one to specify the measure in some applications.

Path‐integral treatment of multi‐mode vibronic coupling. II. Correlation expansion of class averages

1995 ◽  
Vol 102 (16) ◽  
pp. 6499-6510 ◽  
Author(s):  
Stefan Krempl ◽  
Manfred Winterstetter ◽  
Wolfgang Domcke
Keyword(s):  
Path Integral ◽  
Vibronic Coupling ◽  
Integral Treatment ◽  
Multi Mode
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