Lorentz group

Summary

In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz. For example, the following laws, equations, and theories respect Lorentz symmetry:

The kinematical laws of special relativity
Maxwell's field equations in the theory of electromagnetism
The Dirac equation in the theory of the electron
The Standard Model of particle physics

The Lorentz group expresses the fundamental symmetry of space and time of all known fundamental laws of nature. In small enough regions of spacetime where gravitational variances are negligible, physical laws are Lorentz invariant in the same manner as special relativity. Basic properties The Lorentz group is a subgroup of the Poincaré group—the group of all isometries of Minkowski spacetime. Lorentz transformations are, precisely, iso

Official source

https://en.wikipedia.org/wiki/Lorentz_group

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We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed symmetry representations of the Lorentz group, which were inaccessible in previous bootstrap studies. We find discontinuities in some of the bounds on operator dimensions, and we show that they arise due to a generic yet previously unobserved fake primary effect, which is related to the existence of poles in conformal blocks. We show that this effect is also responsible for similar discontinuities found in four-fermion bootstrap in 3d, as well as in the mixed-correlator analysis of the 3d Ising CFT. As an important byproduct of our work, we develop a practical technology for numerical approximation of general 4d conformal blocks.

Springer2019

Spinning operators and defects in conformal field theory

Marco Meineri

We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic representation of the Lorentz group. The recipe yields the explicit structures in embedding space, and can be applied to any correlator of local operators, with or without a defect. We then focus on the two-point function of traceless symmetric primaries in the presence of a conformal defect, and explain how to compute the conformal blocks. In particular, we illustrate various techniques to generate the bulk channel blocks either from a radial expansion or by acting with differential operators on simpler seed blocks. For the defect channel, we detail a method to compute the blocks in closed form, in terms of projectors into mixed symmetry representations of the orthogonal group.

Springer2019

Non-Pauli-Fierz Massive Gravitons

Michele Redi

We study general Lorentz invariant theories of massive gravitons. We show that, contrary to the standard lore, there exist consistent theories where the graviton mass term violates Pauli-Fierz structure. For theories where the graviton is a resonance, this does not imply the existence of a scalar ghost if the deviation from a Pauli-Fierz structure becomes sufficiently small at high energies. These types of mass terms are required by any consistent realization of the Dvali-Gabadadze-Porrati model in higher dimension.

2008