相关论文: Rotations associated with Lorentz boosts
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
A topologically finite universe, smaller than the observable horizon, will have circles-in-the-sky: pairs of circles around which the temperature fluctuations in the cosmic microwave background are correlated. The circles occur along the…
There exist elegant methods of aligning point clouds in $\mathbb R^3$. Unfortunately, these methods fail to generalize to the case of Minkowski space, as we will show. Instead, we propose two solutions to the following problem: given…
If Einstein's photon is $E = cp = \hbar\omega$, Wigner's photon is its helicity which is a Lorentz-invariant concept coming from the E(2)-like little group for massless particles. In addition, the E(2)-like little group has two…
We discuss modifications to the Hawking spectrum that arise when the asymptotic states are supertranslated or superrotated. For supertranslations we find nontrivial off-diagonal phases in the two-point correlator although the emission…
We derive finite boost transformations based on the Lorentz sector of the bicross-product-basis $\kappa$-Poincare' Hopf albegra. We emphasize the role of these boost transformations in a recently-proposed new relativistic theory. We find…
A Lorentz boosted two-nucleon potential is introduced in the context of equal time relativistic quantum mechanics. The dynamical input for the boosted nucleon-nucleon (NN) potential is based on realistic NN potentials, which by a suitable…
Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
Optical response of crystalline solids is to a large extent driven by excitations that promote electrons among individual bands. This allows one to apply optical and magneto-optical methods to determine experimentally the energy band gap -…
Dynamics with noncommutative coordinates invariant under three dimensional rotations or, if time is included, under Lorentz transformations is developed. These coordinates turn out to be the boost operators in SO(1,3) or in SO(2,3)…
A double covering of the proper orthochronous Lorentz group is understood as a complexification of the special unimodular group of second order (a double covering of the 3-dimensional rotation group). In virtue of such an interpretation the…
The rotating frame is considered in quantum mechanics on the basis of the position dependent boost relating this frame to the non rotating inertial frame. We derive the Sagnac phase shift and the spin coupling with the rotation in the non…
The effects of Lorentz boosts on the quantum entanglement encoded by a pair of massive spin one-half particles are described according to the Lorentz covariant structure described by Dirac bispinors. The quantum system considered…
The effect of the relativistic spin rotation, conditioned by the setting of the spin in the rest frame of a particle and by the noncommutativity of the Lorentz transformations along noncolinear directions, is discussed. In connection with…
We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-$\frac12$ particle with definite helicity. We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost…
We identify momentum/helicity probability amplitudes for the photon and find their relativistic transformation properties. We also find their behaviour under space inversion and time reversal. The discussion begins with a review of the…
Traditionally, the interactions related to the 3D spatial angular momentum have been studied completely, while the ones related to the generators of Lorentz boost are always ignored. In this paper we show that the generators of Lorentz…
We show that starting with the fact that special relativity theory is concerned with a distortion of the observed length of a moving rod, without mentioning if it is a "contraction" or "dilation", we can derive the Lorentz transformations…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…