scholarly journals A GAUGE THEORY OF QUANTUM MECHANICS

2007 ◽  
Vol 22 (03) ◽  
pp. 191-200 ◽  
Author(s):  
JOSÉ M. ISIDRO ◽  
MAURICE A. DE GOSSON
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Phase Space ◽  
Gauge Group ◽  
Path Integrals ◽  
Invariance Group ◽  
Feynman Path ◽  
Cartan Form ◽  
Feynman Path Integrals ◽  
Classical Phase Space

An Abelian gerbe is constructed over classical phase space. The two-cocycles defining the gerbe are given by Feynman path integrals whose integrands contain the exponential of the Poincaré–Cartan form. The U(1) gauge group on the gerbe has a natural interpretation as the invariance group of the Schrödinger equation on phase space.

scholarly journals GERBES AND HEISENBERG'S UNCERTAINTY PRINCIPLE

2006 ◽  
Vol 03 (08) ◽  
pp. 1469-1480 ◽  
Author(s):  
JOSÉ M. ISIDRO
Keyword(s):  
Phase Space ◽  
Field Strength ◽  
Uncertainty Principle ◽  
Path Integrals ◽  
Feynman Path ◽  
Feynman Path Integrals ◽  
Form Field ◽  
Classical Phase Space ◽  
Heisenberg's Uncertainty Principle

We prove that a gerbe with a connection can be defined on classical phase space, taking the U(1)-valued phase of certain Feynman path integrals as Čech 2-cocycles. A quantisation condition on the corresponding 3-form field strength is proved to be equivalent to Heisenberg's uncertainty principle.

scholarly journals Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method

2012 ◽  
Vol 50 (3) ◽  
pp. 156-158 ◽  
Author(s):  
María de los Ángeles Fanaro ◽  
María Rita Otero ◽  
Marcelo Arlego
Keyword(s):  
Quantum Mechanics ◽  
Secondary School ◽  
Path Integrals ◽  
Feynman Path ◽  
Feynman Path Integrals

NELSON'S STOCHASTIC MECHANICS BY MEANS OF FEYNMAN PATH INTEGRALS

2000 ◽  
Vol 14 (03) ◽  
pp. 73-78 ◽  
Author(s):  
LUIZ C. L. BOTELHO
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Path Integrals ◽  
Order Equation ◽  
Feynman Path Integral ◽  
Stochastic Mechanics ◽  
Path Integral Formulation ◽  
Feynman Path ◽  
First Order ◽  
Feynman Path Integrals

We show that Nelson's stochastic mechanics suitably formulated as a Hamilton–Jacobi first-order equation leads straightforwardly to the Feynman path integral formulation of quantum mechanics.

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