How to prove that orthochronous Lorentz transformations
The Lorentz group moves the unit time vector somewhere on the hyperboloid: $$ t^2 - x^2 = 1 $$ In however many dimensions. This is a disconnected space, there are two components--- the …
special relativity - Tensor product of representations of Lorentz …
2020年4月13日 · There may be a confusion of the tensor product ⊗ used in both linking the Lorentz Group left ideal A to the right one B but also, again with common rotation angles!, to …
mathematical physics - Representations of the Lorentz group in an ...
2017年9月15日 · $\begingroup$ The Lorentz group is isomorphic to the Euclidean conformal group so the representations you are looking for are basically the highest weight …
special relativity - Lorentz group $SO(3,1)$ and $SU(2)\times SU(2 ...
2016年9月3日 · The theory of Lorentz-group and its representation is rather involved. For more precision and information ...
Lorentz Group Representations - Physics Stack Exchange
2017年3月25日 · Now consider the $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group. This representation has dimension four (implying that we are dealing with four components …
What is the difference between the $Spin(3,1)$ group and the …
2016年1月28日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
quantum field theory - Dimension of representations of Lorentz …
2016年9月28日 · Spin (1/2) gives 2 dimensional matrices, Spin (1) gives 3 dimensional matrices, and so on. But it seems we have lost that uniqueness in the Lorentz group. The vector …
special relativity - The real vs complex Lorentz group and their ...
2019年2月13日 · Ignoring technical difficulties, it doesn't matter as you would want to allow projective representations when talking about quantum physics anyways. An then, classifying …
Infinite dimensional representation of Lorentz group
2021年2月4日 · Since the Lorentz group is not simply connected, this can't be done via exponentiation. Nevertheless, the proper orthochronous Lorentz group …
Vector spaces for the irreducible representations of the Lorentz …
2014年11月29日 · This is isomorphic to the vector representation of the Lorentz group. The Dirac-spinor representation $(\frac{1}{2},0) \oplus (0,\frac{1}{2})$ is a direct sum of the left- and right …