scholarly journals Phase space Feynman path integrals of higher order parabolic type with general functional as integrand

2015 ◽  
Vol 139 (5) ◽  
pp. 495-537 ◽  
Author(s):  
Naoto Kumano-go ◽  
A.S. Vasudeva Murthy
Keyword(s):  
Phase Space ◽  
Path Integrals ◽  
Parabolic Type ◽  
Higher Order ◽  
Feynman Path ◽  
Feynman Path Integrals

scholarly journals Phase space Feynman path integrals

2002 ◽  
Vol 43 (6) ◽  
pp. 2847-2857 ◽  
Author(s):  
S. Albeverio ◽  
G. Guatteri ◽  
S. Mazzucchi
Keyword(s):  
Phase Space ◽  
Path Integrals ◽  
Feynman Path ◽  
Feynman Path Integrals

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.

Generalized Feynman path integrals and applications to higher-order heat-type equations

2018 ◽  
Vol 36 (3-4) ◽  
pp. 406-429
Author(s):  
S. Albeverio ◽  
N. Cangiotti ◽  
S. Mazzucchi
Keyword(s):  
Path Integrals ◽  
Higher Order ◽  
Feynman Path ◽  
Feynman Path Integrals
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