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Related Concept Videos

Base Quantities and Derived Quantities01:14

Base Quantities and Derived Quantities

In any system of units, the units for some physical quantities must be specified through a measurement process. These measurements are the base quantities of the system, and their units are the base units of the system. The algebraic combinations of the base values can then be used to express all other physical quantities. Each of these physical quantities is then referred to as a derived quantity, with each unit being referred to as a derived unit.
The International Organization for...
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Related Experiment Video

Updated: May 16, 2026

Quantifying Branching Density in Rat Mammary Gland Whole-mounts Using the Sholl Analysis Method
11:02

Quantifying Branching Density in Rat Mammary Gland Whole-mounts Using the Sholl Analysis Method

Published on: July 12, 2017

Branched quantization.

Alfred Shapere1, Frank Wilczek

  • 1Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA.

Physical Review Letters
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

We present a new quantization method for Lagrangians with branched Hamiltonians. This approach ensures unitary time evolution and connects to quantum mechanics on singular spaces.

Related Experiment Videos

Last Updated: May 16, 2026

Quantifying Branching Density in Rat Mammary Gland Whole-mounts Using the Sholl Analysis Method
11:02

Quantifying Branching Density in Rat Mammary Gland Whole-mounts Using the Sholl Analysis Method

Published on: July 12, 2017

Area of Science:

  • Theoretical Physics
  • Quantum Mechanics
  • Mathematical Physics

Background:

  • Quantization of physical systems is fundamental in theoretical physics.
  • Branched Hamiltonians present challenges for standard quantization procedures.
  • Unitary time evolution is a key requirement for quantum mechanical descriptions.

Purpose of the Study:

  • To develop a novel method for quantizing Lagrangians with branched Hamiltonians.
  • To establish appropriate boundary conditions for ensuring unitary time evolution.
  • To explore connections between this quantization method and quantum mechanics on singular spaces.

Main Methods:

  • Proposing a specific quantization technique for Lagrangians.
  • Identifying and applying necessary boundary conditions.
  • Developing dual (canonical) transformations for special cases.

Main Results:

  • A method for quantizing Lagrangians with branched Hamiltonians is established.
  • Unitary time evolution is guaranteed through identified boundary conditions.
  • A mapping to quantum mechanics on singular spaces is demonstrated.

Conclusions:

  • The proposed method provides a viable approach for quantizing complex Lagrangians.
  • The framework offers new insights into quantum mechanics on singular spaces.
  • Potential applications in various areas of physics are suggested.