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Spinnor
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I'm thinking of an object or objects. How do I show that the objects form a representation of the Lorentz group in 1+1 D spacetime?
Thanks for any help!
Thanks for any help!
Spinnor said:I'm thinking of an object or objects. How do I show that the objects form a representation of the Lorentz group in 1+1 D spacetime?
Thanks for any help!
Dunno if this will help, but, to clarify some terminology,...Spinnor said:From a Google search "spinor representation of the lorentz group" it looks like spinors are the representations? I'm confused.
strangerep said:Dunno if this will help, but, to clarify some terminology,...
A "representation" in this context means a mapping from the abstract group elements to concrete matrices acting on a vector space. The vector space is then said to "carry the representation". In your case, the space of spinors "carries" a representation of the Lorentz group in terms of 2x2 matrices acting on that space.
Spinnor said:From http://arxiv.org/pdf/0912.2560.pdf we are given,
Λ = e(iθµνMµν) , which in the 1+1D spacetime simplifies to
Λ = e(iθM)?
The same Λ then acts on both 2 dimensional vectors in 2 dimensional Minkowski spacetime, but also the space of 2 component complex spinors?
In this case is Λ the "concrete" matrix? If so what are the abstract elements in this case?
Historically, which representation came first?
Thanks for your help!
The Lorentz Group can be represented by objects that exhibit certain properties, such as being invariant under Lorentz transformations and having a maximum speed of light. Additionally, objects that follow the laws of special relativity, such as the conservation of energy and momentum, also represent the Lorentz Group.
No, not all physical objects can represent the Lorentz Group. The Lorentz Group is specific to objects that follow the principles of special relativity, which govern the behavior of objects moving at high speeds. Objects that do not experience relativistic effects, such as stationary objects, do not represent the Lorentz Group.
There are no visual cues that can definitively determine if an object represents the Lorentz Group. The properties and behaviors of the object must be examined to determine if it follows the principles of special relativity.
The Lorentz Group is closely related to the laws of special relativity, which are fundamental principles of physics that govern the behavior of objects moving at high speeds. The Lorentz Group is a mathematical representation of these laws and helps to explain the behavior of objects in these scenarios.
The Lorentz Group is primarily used to describe the behavior of objects moving at high speeds, such as particles in particle accelerators. While some aspects of the Lorentz Group may apply to everyday objects, such as the speed of light being the maximum speed, the full extent of its principles are not applicable to everyday situations.