Path integral representation for inelastic scattering amplitude and its quasiclassical approximations

1977 ◽  
Vol 30 (2) ◽  
pp. 146-152 ◽  
Author(s):  
A. V. Bogdanov ◽  
G. V. Dubrovskii
Keyword(s):  
Integral Representation ◽  
Inelastic Scattering ◽  
Path Integral ◽  
Scattering Amplitude ◽  
Path Integral Representation

Quantum evolution: From particles to non-relativistic fields

2021 ◽  
pp. 90-104
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Particle Physics ◽  
Evolution Operator ◽  
Scattering Amplitude ◽  
Eikonal Approximation ◽  
Functional Integral ◽  
Quantum Evolution ◽  
Path Integral Representation ◽  
Functional Integral Representation

Chapter 4 has introduced the functional integral representation of the quantum statistical operators and thus, formally, evolution in imaginary or Euclidean time. By contrast, to calculate the evolution operator and the scattering S-matrix elements, quantities relevant to particle physics, it is necessary to make a continuation from imaginary to real time. However, the representation of the S-matrix follows from additional considerations. To illustrate the power of the formalism, we show how to recover the perturbative expansion of the scattering amplitude, some semi-classical approximations, and the eikonal approximation. When the asymptotic states at large time are eigenstates of the harmonic oscillator, instead of free particles, the holomorphic formalism becomes useful. A simple generalization of the path integral of Chapter 4 leads to the corresponding path integral representation of the S-matrix. In the case of the Bose gas, the evolution operator is then given by a holomorphic field integral. A parallel formalism leads to an analogous representation for the evolution operator of a system of non-relativistic fermions.

scholarly journals Path integral representation of the evolution operator for the Dirac equation

2006 ◽  
Author(s):  
Alexander S. Lukyanenko ◽  
Inna A. Lukyanenko
Keyword(s):  
Dirac Equation ◽  
Integral Representation ◽  
Path Integral ◽  
Evolution Operator ◽  
Path Integral Representation

Path-integral representation for tunneling amplitudes in the Schwinger model

1979 ◽  
Vol 117 (2) ◽  
pp. 382-392 ◽  
Author(s):  
K.D Rothe ◽  
J.A Swieca
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Path Integral Representation ◽  
Schwinger Model

ANOTHER DERIVATION OF A SUPERPARTICLE ACTION

1991 ◽  
Vol 06 (21) ◽  
pp. 1977-1982 ◽  
Author(s):  
E. S. FRADKIN ◽  
SH. M. SHVARTSMAN
Keyword(s):  
Green Function ◽  
Integral Representation ◽  
Path Integral ◽  
Path Integral Representation ◽  
Chiral Superfield

It is shown that the reparametrization invariant superparticle action can be determined by constructing the path-integral representation for the causal Green function of a chiral superfield interacting with an external Maxwell superfield.

Perturbation theory in the path-integral representation and its application to some simple quantum systems

1977 ◽  
Vol 12 (2) ◽  
pp. 233-246
Author(s):  
Y. U. E. Perlin ◽  
S. H. N. Gifeisman ◽  
Pham Van Quyet
Keyword(s):  
Perturbation Theory ◽  
Integral Representation ◽  
Path Integral ◽  
Quantum Systems ◽  
Path Integral Representation ◽  
Simple Quantum

scholarly journals Euclidean Path-Integral Representation of Linearized Gravitational Field

1989 ◽  
Vol 82 (4) ◽  
pp. 791-803
Author(s):  
H. Fukutaka ◽  
T. Kashiwa
Keyword(s):  
Gravitational Field ◽  
Integral Representation ◽  
Path Integral ◽  
Path Integral Representation

scholarly journals SUPERSYMMETRY, HOMOLOGY WITH TWISTED COEFFICIENTS AND n-DIMENSIONAL KNOTS

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4185-4196 ◽  
Author(s):  
EIJI OGASA
Keyword(s):  
Integral Representation ◽  
Natural Number ◽  
Quantum System ◽  
Path Integral ◽  
Topological Invariant ◽  
Supersymmetric Theory ◽  
Path Integral Representation ◽  
Alexander Polynomials ◽  
Usual Manner ◽  
Infinitesimal Transformations

In this paper, we study and construct a set of Witten indexes for K, where K is any n-dimensional knot in Sn+2 and n is any natural number. We form a supersymmetric quantum system for K by, first, constructing a set of functional spaces (spaces of fermionic (resp. bosonic) states) and a set of operators (supersymmetric infinitesimal transformations) in an explicit way. Our Witten indexes are topological invariant and they are nonzero in general. These indexes are zero if K is equivalent to a trivial knot. Besides, our Witten indexes restrict to the Alexander polynomials of n-knots, and one of the Alexander polynomials of K is nontrivial if any of the Witten indexes is nonzero. Our indexes are related to homology with twisted coefficients. Roughly speaking, these indexes posseses path-integral representation in the usual manner of supersymmetric theory.

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