Path integral representation for the solution of a stochastic Schrodinger equation driven by a semimartingale

2004 ◽  
Vol 7 (2) ◽  
pp. 183-204 ◽  
Author(s):  
L. A. Rincón
Keyword(s):  
Schrödinger Equation ◽  
Integral Representation ◽  
Path Integral ◽  
Schrodinger Equation ◽  
Path Integral Representation ◽  
Stochastic Schrödinger Equation

A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations

2002 ◽  
Vol 132 (2) ◽  
pp. 353-375 ◽  
Author(s):  
VASSILI N. KOLOKOLTSOV
Keyword(s):  
Hilbert Space ◽  
Schrödinger Equation ◽  
Integral Representation ◽  
Path Integral ◽  
Schrodinger Equation ◽  
Path Space ◽  
Schrödinger Equations ◽  
Path Integral Representation ◽  
Stochastic Schrödinger Equation ◽  
Finite Measures

Solutions to the Schrödinger, heat and stochastic Schrödinger equation with rather general potentials are represented, both in x- and p-representations, as integrals over the path space with respect to σ-finite measures. In the case of x-representation, the corresponding measure is concentrated on the Cameron–Martin Hilbert space of curves with L2-integrable derivatives. The case of the Schrödinger equation is treated by means of a regularization based on the introduction of either complex times or continuous non-demolition observations.

Continuous Quantum Measurement: Local and Global Approaches

1997 ◽  
Vol 09 (08) ◽  
pp. 907-920 ◽  
Author(s):  
S. Albeverio ◽  
V. N. Kolokol'tsov ◽  
O. G. Smolyanov
Keyword(s):  
Schrödinger Equation ◽  
Quantum System ◽  
Quantum Measurement ◽  
Path Integral ◽  
Schrodinger Equation ◽  
Stochastic Equation ◽  
Point Of View ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Stochastic Schrödinger Equation

In 1979 B. Menski suggested a formula for the linear propagator of a quantum system with continuously observed position in terms of a heuristic Feynman path integral. In 1989 the aposterior linear stochastic Schrödinger equation was derived by V. P. Belavkin describing the evolution of a quantum system under continuous (nondemolition) measurement. In the present paper, these two approaches to the description of continuous quantum measurement are brought together from the point of view of physics as well as mathematics. A self-contained deductions of both Menski's formula and the Belavkin equation is given, and the new insights in the problem provided by the local (stochastic equation) approach to the problem are described. Furthermore, a mathematically well-defined representations of the solution of the aposterior Schrödinger equation in terms of the path integral is constructed and shown to be heuristically equivalent to the Menski propagator.

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.

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