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Contextual and Cued Fear Conditioning Test Using a Video Analyzing System in Mice
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Generalized Fock space and contextuality.

Sergey Rashkovskiy1,2, Andrei Khrennikov3,4

  • 1Ishlinsky Institute for Problems in Mechanics RAS, Vernadskogo Ave., 101/1, Moscow 119526, Russia.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|September 17, 2019
PubMed
Summary
This summary is machine-generated.

This study represents contextual probabilities using linear spaces in generalized Fock space. This approach allows for the expression of probabilistic dynamics and reproduces the Doi-Peliti formalism.

Keywords:
Doi-Peliti formalismFock spacecalculi of creation–annihilation operatorscontextualityinterference of probabilitiesquantum probability

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Area of Science:

  • Quantum mechanics
  • Probability theory
  • Mathematical physics

Background:

  • Contextuality is a key feature in quantum mechanics.
  • Probabilistic dynamics are often described using complex mathematical frameworks.
  • The Doi-Peliti formalism is a significant tool for analyzing stochastic processes.

Purpose of the Study:

  • To develop linear space representations for contextual probabilities.
  • To utilize creation and annihilation operators for probabilistic dynamics.
  • To quantify context-dependence using an interference term.

Main Methods:

  • Employing generalized Fock space for probability representation.
  • Applying the calculus of creation and annihilation operators.
  • Generalizing the formula of total probability.

Main Results:

  • Linear space representations of contextual probabilities are established.
  • Probabilistic dynamics, including classical kinetic equations, are expressed within Fock space.
  • The Doi-Peliti formalism is successfully reproduced.
  • A method to quantify probability context-dependence via an interference term is presented.

Conclusions:

  • Linear space representations offer a powerful framework for contextual probabilities.
  • The calculus of creation and annihilation operators provides a versatile tool for probabilistic dynamics.
  • This work bridges quantum mechanics and probability theory, offering new insights into contextuality.