Koopman-von Neumann formulation of classical Yang-Mills theories: I

Carta, Paolo; Gozzi, E.; Mauro, D.

doi:10.1002/andp.200510177

Cited by 14 publications

(15 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…0. Since~enters in the time derivative of Schödinger equation (17) as well as in the commutator relationship (15), the limit~! 0 encompasses more than the criterion that the coordinate and momentum operators must commute in the classical limit.…”

Section: Commutator Eqsmentioning

confidence: 99%

See 1 more Smart Citation

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

et al. 2012

View full text Add to dashboard Cite

We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

show abstract

Section: Commutator Eqsmentioning

confidence: 99%

“…(The Koopman-von Neumann approach has been extended to classical field theories in Refs. [17,19,20]. )…”

Section: Classical Field Theorymentioning

confidence: 99%

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

et al. 2012

View full text Add to dashboard Cite

show abstract

“…include Refs. 20,21,22,23,24. It should be emphasized that the Koopman-von Neumann-Sudarshan theory is not the → 0 limit of QM.…”

Section: 1415mentioning

confidence: 99%

Quantum ${{\mathbb{F}}_{{\rm un}}}$: theq= 1 limit of Galois field quantum mechanics, projective geometry and the field with one element

Chang

Lewis

Minić

et al. 2014

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We argue that the q = 1 limit of Galois Field Quantum Mechanics, which was constructed on a vector space over the Galois Field Fq = GF (q), corresponds to its 'classical limit,' where superposition of states is disallowed. The limit preserves the projective geometry nature of the state space, and can be understood as being constructed on an appropriately defined analogue of a 'vector' space over the 'field with one element' F 1 .

show abstract

“…We will show in this paper that the answer lies in the classic works of Koopman [9], von Neumann [10] and later others [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. Sudarshan [26] developed a complete theory of Classical Mechanics (CM) based on Hilbert spaces associated with commuting hermitian operators as observables (hereinafter referred to as the KvNS theory).…”

Section: Introductionmentioning

confidence: 99%

Hilbert space theory of classical electrodynamics

Rajagopal

Ghose

2016

Pramana - J Phys

View full text Add to dashboard Cite

Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman-von Neumann-Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commuting observables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of much recent work on quantum-like features exhibited by classical optics. Furthermore, following Bondar et al (Phys.Rev. A 88, 052108, (2013)), it is pointed out that quantum processes that preserve the positivity or nonpositivity of the Wigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.

show abstract

Koopman-von Neumann formulation of classical Yang-Mills theories: I

Cited by 14 publications

References 32 publications

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

Quantum ${{\mathbb{F}}_{{\rm un}}}$: theq= 1 limit of Galois field quantum mechanics, projective geometry and the field with one element

Hilbert space theory of classical electrodynamics

Contact Info

Product

Resources

About