On the Meaning of the String-Inspired Noncommutativity and its Implications

Abstract

We propose an alternative interpretation for the meaning of noncommutativity of the string-inspired field theories and quantum mechanics. Arguments are presented to show that the noncommutativity generated in the stringy context should be assumed to be only between the particle coordinate observables, and not of the spacetime coordinates. Some implications of this fact for noncomutative field theories and quantum mechanics are discussed. In particular, a consistent interpretation is given for the wavefunction in quantum mechanics. An analysis of the noncommutative theories in the Schrödinger formulation is performed employing a generalized quantum Hamilton-Jacobi formalism. A formal structure for noncommutative quantum mechanics, richer than the one of noncommutative quantum field theory, comes out. Conditions for the classical and commutative limits of these theories have also been determined and applied in some examples.

References, comments, and footnotes are included; some changes in section 5

References in corpus (2)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Quantum Equilibrium and the Origin of Absolute Uncertainty

Cited by in corpus (6)

• Noncommutative Geometry and Cosmology
• Noncommutative Conformally Coupled Scalar Field Cosmology and its Commutative Counterpart
• Noncommutative quantum mechanics and Bohm's ontological interpretation
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces
• Quantum mechanics on non commutative spaces and squeezed states: a functional approach