Boost Generators: Physical Meaning & Observable Quantities

In summary, the generators of the Poincare group, which include time translation, space translations, rotations, and boosts, are associated with well-known physical quantities such as energy, momentum, and angular momentum. However, the distinction between boosts and rotations is frame-dependent, and when they are unified, there is a relativistic angular momentum tensor that corresponds to these generators. This concept is further explained on Wikipedia's page on relativistic angular momentum.
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nicholas_eng
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TL;DR Summary
Do the generators of boosts correspond to anything physical?
So, all of the generators of the Poincare group are associated with pretty well-known physical quantities. Time translation is associated with energy, space translations with momentum, rotations with angular momentum, and boosts... well, boosts are generated by the "generators of boosts". Do they correspond to any observable?
 
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A proper understanding of boosts in the context of your question requires unifying them with rotations; note that the split between what is a "boost" and what is a "rotation" is frame-dependent. When we unify boosts and rotations, we find that there is a relativistic angular momentum tensor that corresponds to the boost/rotation generators. Wikipedia has a brief discussion:

https://en.wikipedia.org/wiki/Relat...e_generator_of_spacetime_boosts_and_rotations
 
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FAQ: Boost Generators: Physical Meaning & Observable Quantities

What is the physical meaning of boost generators?

Boost generators are a set of mathematical operators that describe the transformation of physical quantities, such as position and momentum, under boosts in special relativity. They represent the change in these quantities as an object moves at a constant velocity relative to an observer.

How are boost generators related to Lorentz transformations?

Lorentz transformations are a type of mathematical transformation that describes how physical quantities change between two frames of reference in special relativity. Boost generators are the generators of these transformations, meaning they can be used to derive the full set of Lorentz transformations.

What are some observable quantities that can be derived from boost generators?

Some observable quantities that can be derived from boost generators include time dilation, length contraction, and relativistic momentum. These quantities describe the effects of special relativity on physical systems moving at high speeds.

How do boost generators affect the behavior of particles at high speeds?

Boost generators play a crucial role in understanding the behavior of particles at high speeds. They show how quantities such as energy and momentum change as an object approaches the speed of light. This is important in fields such as particle physics, where particles can reach speeds close to the speed of light.

Are boost generators applicable in other areas of physics?

While boost generators were originally developed for use in special relativity, they have also found applications in other areas of physics. For example, they are used in quantum field theory to study the behavior of particles and fields at high energies. They also have applications in classical mechanics, where they can be used to describe the motion of objects in a rotating reference frame.

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