• Corpus ID: 119204305

The Dirac-Bohm Picture

@article{Hiley2018TheDP,
  title={The Dirac-Bohm Picture},
  author={Basil J. Hiley and Glen Dennis},
  journal={arXiv: Quantum Physics},
  year={2018}
}
We examine Dirac's early algebraic approach which introduces the {\em standard} ket and show that it emerges more clearly from a unitary transformation of the operators based on the action. This establishes a new picture that is unitarily equivalent to both the Schrodinger and Heisenberg pictures. We will call this the Dirac-Bohm picture for the reasons we discuss in the paper. This picture forms the basis of the Feynman path theory and allows us to show that the so-called `Bohm trajectories… 
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References

SHOWING 1-10 OF 38 REFERENCES

Schrodinger revisited: the role of Dirac's 'standard' ket in the algebraic approach

We follow Dirac and write the Schrödinger equation in an algebraic form which is representation-free. The imaginary and real parts of this equation are respectively the Liouville equation, which

Feynman Paths and Weak Values

It is concluded that a Bohm ‘trajectory’ is the average of an ensemble of actual individual stochastic Feynman paths, which implies that they can be interpreted as the mean momentum flow of a set of individual quantum processes and not the path of an individual particle.

Algebras, Quantum Theory and Pre-space

The relationship between the algebraic formulation of quantum mechanics, algebraic geometry and pre-space, a notion that arises in Bohm's implicate order, is discussed with particular reference to

Clifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation

In this paper we show how the dynamics of the Schrödinger, Pauli and Dirac particles can be described in a hierarchy of Clifford algebras, ${\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}$, and

Imprints of the Quantum World in Classical Mechanics

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show that the Schrödinger equation for a nonrelativistic spinless

The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics

1. Quantum mechanics and its interpretation 2. Hamilton-Jacobi theory 3. Elements of the quantum theory of motion 4. Simple applications 5. Interference and tunnelling 6. The classical limit 7.

The Principles of Quantum Mechanics

IT is now twenty years since the theory of quantum mechanics was founded, and not much less since the first edition of Dirac's book was published. Ever since, it has been a classic of scientific

Geometrization of Quantum Mechanics and the New Interpretation of the Scalar Product in Hilbert Space

It is shown that the new interpretation of the scalar product in Hilbert space recently proposed by Aharanov, Albert, and Au is in fact the one underlying the stochastic phase-space formulation of

What Is Bohmian Mechanics

Bohmian mechanics is a quantum theory with a clear ontology and the status and the role of of the quantum formalism is clarified.