2003
DOI: 10.1016/s0003-4916(03)00145-3
|View full text |Cite
|
Sign up to set email alerts
|

The role of phase space geometry in Heisenberg’s uncertainty relation

Abstract: Aiming towards a geometric description of quantum theory, we study the coherent states-induced metric on the phase space, which provides a geometric formulation of the Heisenberg uncertainty relations (both the position-momentum and the time-energy ones). The metric also distinguishes the original uncertainty relations of Heisenberg from the ones that are obtained from non-commutativity of operators. Conversely, the uncertainty relations can be written in terms of this metric only, hence they can be formulated… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
4
1

Citation Types

0
19
0

Year Published

2003
2003
2016
2016

Publication Types

Select...
8

Relationship

4
4

Authors

Journals

citations
Cited by 10 publications
(19 citation statements)
references
References 50 publications
0
19
0
Order By: Relevance
“…In previous work [4], we proved that the condition δs 2 ∼ 1 is equivalent to the Heisenberg uncertainty relations. The metric together with the connection allow the determination of the coherent state propagator z|e −iĤt |z ′ by means of a path integral…”
Section: Generalised Coherent Statesmentioning
confidence: 75%
See 2 more Smart Citations
“…In previous work [4], we proved that the condition δs 2 ∼ 1 is equivalent to the Heisenberg uncertainty relations. The metric together with the connection allow the determination of the coherent state propagator z|e −iĤt |z ′ by means of a path integral…”
Section: Generalised Coherent Statesmentioning
confidence: 75%
“…Its role is twofold. First it determines the resolution of phase space measurements thus implementing the Heisenberg uncertainty relation [4]. Second, it is a crucial ingredient of the coherent state path integral [5,6], because it defines a Wiener process through which the path integral may be regularised.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…There has been a continual interest in utilizing HUP in different settings. For example, it has been used in the study of central potentials [7]- [11] and others consider its connection to geometry [12] [13]. Furthermore, it has been generalized to describe a minimal length as a minimal uncertainty in position measurement [14]- [18] through the modification of Heisenberg commutation relation into a generalized form.…”
Section: Introductionmentioning
confidence: 99%
“…, when the quantum objects are complementarily manifested either as wave or particle ) nor with the wave-particle equivalency in free evolution (that is not necessarily related with free motion but with quantum existence independent of any experiment or observation). Nevertheless, possible generalizations and reformulation of HUR were suggested during the last decade by the modern quantum mathematics [ 10 12 ], optics [ 13 ], information theory [ 14 16 ], still without establishing the HUR description in the absence of commutation rules [ 17 , 18 ] or versions of Schwarz inequality [ 19 , 20 ].…”
Section: Introductionmentioning
confidence: 99%