Is Canonical Momentum conserved?

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Thread starter LarryS
Start date Jun 18, 2016
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Em Lagrangian mechanics Momentum Momentum conservation

In summary, canonical momentum is a concept in physics that refers to the momentum of a particle in a particular coordinate system. It is derived from Hamiltonian mechanics and is also known as conjugate momentum. While it is conserved in systems with a symmetric potential and no external forces, it may change in other cases due to interactions with other particles or fields. Canonical momentum is related to kinetic energy through the Hamiltonian function, which is used to derive the equations of motion for a system. Its units depend on the system of measurement used, and it can also be extended to other physical systems, such as fields and waves, where it is defined as the momentum density of the system. The conservation of canonical momentum still applies in these cases.

Jun 18, 2016

LarryS

Gold Member

Given a system of charged particles interacting with an EM field. Is the canonical momentum always conserved? If so, what is the associated symmetry?

Thanks in advance.

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Jun 18, 2016

vanhees71

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The canonical momentum is conserved, if the Hamiltonian is independent of the corresponding configuration variable. Then the system is symmetric under translations of this configuration variable.

Related to Is Canonical Momentum conserved?

1. What is canonical momentum?

Canonical momentum is a concept in physics that refers to the momentum of a particle in a particular coordinate system. It is derived from the Hamiltonian mechanics and is also known as conjugate momentum.

2. Is canonical momentum always conserved?

No, canonical momentum is not always conserved. It is conserved only in systems that have a symmetric potential and do not have external forces acting on them. In other cases, it may change due to interactions with other particles or fields.

3. How is canonical momentum related to kinetic energy?

Canonical momentum is related to kinetic energy through the Hamiltonian function, which is the sum of the kinetic and potential energies of a system. The Hamiltonian function is used to derive the equations of motion for a system, which includes the conservation of canonical momentum.

4. What are the units of canonical momentum?

The units of canonical momentum depend on the system of measurement used. In the SI system, it is measured in kilogram meters per second (kg·m/s), while in the CGS system, it is measured in gram centimeters per second (g·cm/s).

5. Can the concept of canonical momentum be applied to systems other than particles?

Yes, the concept of canonical momentum can be extended to other physical systems, such as fields and waves. In these cases, the canonical momentum is defined as the momentum density of the system, which is the product of the velocity and the energy density of the system. The conservation of canonical momentum is still applicable in these cases.