scholarly journals PATH INTEGRAL QUANTIZATION OF THE SYMPLECTIC LEAVES OF THE SU(2)* POISSON–LIE GROUP

1999 ◽  
Vol 14 (06) ◽  
pp. 919-936 ◽  
Author(s):  
BOGDAN MORARIU
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Lie Group ◽  
Unitary Representations ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Path Integral Quantization ◽  
Symplectic Leaves

The Feynman path integral is used to quantize the symplectic leaves of the Poisson–Lie group SU(2)*. In this way we obtain the unitary representations of [Formula: see text]. This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. I also compare the results with the path integral quantization of spin.

QuantumSO(3)-invariants dominate theSU(2)-invariant of Casson and Walker

1995 ◽  
Vol 117 (2) ◽  
pp. 237-249 ◽  
Author(s):  
Hitoshi Murakami
Keyword(s):  
Path Integral ◽  
Lie Group ◽  
Mathematical Proof ◽  
Topological Invariants ◽  
Compact Lie Group ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Chern Simons

For a compact Lie groupG, E. Witten proposed topological invariants of a threemanifold (quantumG-invariants) in 1988 by using the Chern-Simons functional and the Feynman path integral [30]. See also [2]. N. Yu. Reshetikhin and V. G. Turaev gave a mathematical proof of existence of such invariants forG=SU(2) [28]. R. Kirby and P. Melvin found that the quantumSU(2)-invariantassociated toq= exp(2π √ − 1/r) withrodd splits into the product of the quantumSO(3)-invariantand[15]. For other approaches to these invariants, see [3, 4, 5, 16, 22, 27].

FEYNMAN PATH-INTEGRAL FOR THE SUM OF THE GLOBAL AND LOCAL KAC-MOODY CHARACTERS

1993 ◽  
Vol 08 (26) ◽  
pp. 2449-2455 ◽  
Author(s):  
BELAL E. BAAQUIE
Keyword(s):  
Compact Group ◽  
Path Integral ◽  
Unitary Representations ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Functional Differential ◽  
Global And Local

Global Kac-Moody characters are defined for arbitrary maps from S1 to G. A pathintegral expression is obtained for the sum over the unitary representations of the global and local Kac-Moody characters for an arbitrary compact group using a functional differential realization of the Kac-Moody generators. The U(1) case is then solved exactly, and the global characters for a given representation are obtained.

THE PHASE SPACE FEYNMAN PATH INTEGRAL WITH GAUGE INVARIANCE AND ITS CONVERGENCE

2000 ◽  
Vol 12 (11) ◽  
pp. 1451-1463 ◽  
Author(s):  
WATARU ICHINOSE
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Path Integral ◽  
Gauge Invariance ◽  
Electromagnetic Potential ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Electromagnetic Potentials ◽  
Time Slicing

Convergence of a time-slicing approximation is studied in a general way of the Feynman path integral in phase space with an electromagnetic potential. In the present paper a new approximation of the Feynman path integral in phase space, different from the familiar one in physics, is proposed so that its convergence can be shown independently of the choice of electromagnetic potentials and that gauge invariance of the Feynman path integral defined by its limit can be shown directly. It is also shown that the Feynman path integral in phase space defined above can be expressed in the form of the Feynman path integral in configuration space defined in the familiar way in physics, which Feynman himself stated heuristically.

PATH INTEGRAL APPROACH TO A SINGLE POLYMER CHAIN WITH RANDOM MEDIA

2004 ◽  
Vol 18 (10n11) ◽  
pp. 1465-1478 ◽  
Author(s):  
CH. KUNSOMBAT ◽  
V. SA-YAKANIT
Keyword(s):  
Polymer Chain ◽  
Path Integral ◽  
Random Media ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Short Range Correlation ◽  
Range Correlation ◽  
End Distance ◽  
Non Local ◽  
The Mean

In this paper we consider the problem of a polymer chain in random media with finite correlation. We show that the mean square end-to-end distance of a polymer chain can be obtained using the Feynman path integral developed by Feynman for treating the polaron problem and successfuly applied to the theory of heavily doped semiconductor. We show that for short-range correlation or the white Gaussian model we derive the results obtained by Edwards and Muthukumar using the replica method and for long-range correlation we obtain the result of Yohannes Shiferaw and Yadin Y. Goldschimidt. The main idea of this paper is to generalize the model proposed by Edwards and Muthukumar for short-range correlation to finite correlation. Instead of using a replica method, we employ the Feynman path integral by modeling the polymer Hamiltonian as a model of non-local quadratic trial Hamiltonian. This non-local trial Hamiltonian is essential as it will reflect the translation invariant of the original Hamiltonian. The calculation is proceeded by considering the differences between the polymer propagator and the trial propagator as the first cumulant approximation. The variational principle is used to find the optimal values of the variational parameters and the mean square end-to-end distance is obtained. Several asymptotic limits are considered and a comparison between this approaches and replica approach will be discussed.

A REPRESENTATION OF THE BELAVKIN EQUATION VIA PHASE SPACE FEYNMAN PATH INTEGRALS

2004 ◽  
Vol 07 (04) ◽  
pp. 507-526 ◽  
Author(s):  
S. ALBEVERIO ◽  
G. GUATTERI ◽  
S. MAZZUCCHI
Keyword(s):  
Phase Space ◽  
Continuous Measurement ◽  
Quantum Particle ◽  
Oscillatory Integral ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Infinite Dimensional ◽  
Feynman Path Integrals ◽  
Characteristics Method ◽  
Stochastic Characteristics

The Belavkin equation, describing the continuous measurement of the momentum of a quantum particle, is studied. The existence and uniqueness of its solution is proved via analytic tools. A stochastic characteristics method is applied. A rigorous representation of the solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on the phase space is also given.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

2010 ◽  
Vol 25 (02) ◽  
pp. 135-141
Author(s):  
H. A. ELEGLA ◽  
N. I. FARAHAT
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Path Integral ◽  
Equations Of Motion ◽  
Singular System ◽  
Constrained Systems ◽  
Classical Structure ◽  
Path Integral Quantization ◽  
Total Differential

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

Sign in / Sign up

Export Citation Format

Share Document