Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “LORENTZ TRANSFORMATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics↗
DOE OSTI2019

Lorentz transformations of the thermodynamic quantities

In modern physics there exist several formulations of relativistic thermodynamics of a moving body. The Planck and Ott formalisms are the main ones. However, it is not clear which one is correct. In the present paper, we have solved this problem. We have required the equivalence of the dynamical Hamiltonian of a system to the fundamental thermodynamic potential in addition to the principle of entropy invariance and derived the first law of thermodynamics from this fundamental potential. We have found that in the case of momentum being an independent variable in the Hamiltonian, the Lorentz transformations of the thermodynamic quantities belong to the Planck formalism. However, if we suppose that the velocity is an independent variable in the Hamiltonian (though it is not correct from the point of view of the relativistic dynamics), the Lorentz transformations of the thermodynamic quantities belong to the Ott formalism. It demonstrates that the Ott formalism cannot be appropriate. Moreover, we have proved that in the Planck description the first law of thermodynamics is covariant and the Legendre transform of the Lagrangian is preserved. However, in the Ott description the first law of thermodynamics is not covariant and the Legendre transform is violated. Thus we have demonstrated that only the Planck formulation of relativistic thermodynamics of a moving body is properly defined and the Ott formalism should be discarded.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

Extending the Lorentz transformation by characteristic coordinates

The problem considered is that of rectilinear motion with variable velocity. The paper gives, by an elementary construction, a system of coordinates which is conformal in a restricted region near the axis of the motion. In such coordinates the velocity of light remains invariant even for observers moving with variable velocity. By a particular choice of the scale relation the restricted conformal transformations can be made to reduce to the Lorentz transformation everywhere in the case of constant velocity and locally in the case of variable velocity.

Jones, R. T.↗
NASA NTRS1959

Extending the Lorentz Transformation to Motion with Variable Velocity

The problem considered is that of rectilinear motion with variable velocity. The paper gives, by an elementary construction, a system of coordinates which is conformal in the vicinity of the axis of motion. By a particular choice of the scale relation, such restricted conformal transformations can be made to reduce to the Lorentz transformation everywhere in the case of uniform velocity and locally in the case of variable velocity.

Jones, Robert T.↗
NASA NTRS1988

Dual properties of spacetime under an alternative Lorentz transformation

A coordinate time, t(A), with absolute synchronization is defined as an alternative fourth spatial coordinate for model universes with flat space-time, and the theoretical implications of t(A) are explored in detail. Particular attention is given to a t(A)-based reformulation of the Lorentz transformation, the generalized Galilean transformation, which is found to offer significant advantages in understanding special-relativistic phenomena such as length contraction, time dilation, and the interaction of objects with the physical vacuum. With respect to astrophysical observations of superluminal motion, it is shown that the problem of causality violation can be avoided; the theory also predicts that weak anisotropic effects may be detectable in the earth reference frame.

Chang, T.↗
DOE OSTI2020

Effect of Thomas Rotation on the Lorentz Transformation of Electromagnetic fields

A relativistic particle undergoing successive boosts which are non collinear will experience a rotation of its coordinate axes with respect to the boosted frame. This rotation of coordinate axes is caused by a relativistic phenomenon called Thomas Rotation. We assess the importance of Thomas rotation in the calculation of physical quantities like electromagnetic fields in the relativistic regime. We calculate the electromagnetic field tensor for general three dimensional successive boosts in the particle’s rest frame as well as the laboratory frame. We then compare the electromagnetic field tensors obtained by a direct boost β δβ → + → and successive boosts β → and Δβ → and check their consistency with Thomas rotation. This framework might be important to situations such as the calculation of frequency shifts for relativistic spin1/2 particles undergoing Larmor precession in electromagnetic fields with small field non-uniformities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1996

Two Different Squeeze Transformations

Lorentz boosts are squeeze transformations. While these transformations are similar to those in squeezed states of light, they are fundamentally different from both physical and mathematical points of view. The difference is illustrated in terms of two coupled harmonic oscillators, and in terms of the covariant harmonic oscillator formalism.

Han, D.↗
DOE OSTI2017

Angular momentum conservation law in light-front quantum field theory

We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that j 3 , the z -component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j 3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Oscillators in a (2+1)-dimensional noncommutative space

We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncommutative space where the noncommutativity is induced by the shift of the dynamical variables with generators of SL(2,R) in a unitary irreducible representation considered in Falomir et al. [Phys. Rev. D 86, 105035 (2012)]. This redefinition is interpreted in the framework of the Levi's decomposition of the deformed algebra satisfied by the noncommutative variables. The Hilbert space gets the structure of a direct product with the representation space as a factor, where there exist operators which realize the algebra of Lorentz transformations. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters, finding no constraints between coordinates and momenta noncommutativity parameters. Since the representation space of the unitary irreducible representations SL(2,R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Dressed vs. pairwise states, and the geometric phase of monopoles and charges

We construct the Faddeev-Kulish dressed multiparticle states of electrically and magnetically charged particles, incorporating the effects of real and virtual soft photons. We calculate the properties of such dressed states under Lorentz transformations, and find that they can be identified with the pairwise multi-particle states that transform under the pairwise little group. The shifts in the dressing factors under Lorentz transformations are finite and have a simple geometric interpretation. Using the transformation properties of the dressed states we also present a novel, fully quantum field theoretic derivation of the geometric (Berry) phase obtained by an adiabatic rotation of the Dirac string, and also of the Dirac quantization condition. For half integer pairwise helicity, we show that these multiparticle states have flipped spin-statistics, reproducing the surprising fact that fermions can be made out of bosons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1991

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 2: Development of theory for wing shielding

A unified theory for aerodynamics and noise of advanced turboprops is presented. The theory and a computer code developed for evaluation at the shielding benefits that might be expected by an aircraft wing in a wing-mounted propeller installation are presented. Several computed directivity patterns are presented to demonstrate the theory. Recently with the advent of the concept of using the wing of an aircraft for noise shielding, the case of diffraction by a surface in a flow has been given attention. The present analysis is based on the case of diffraction of no flow. By combining a Galilean and a Lorentz transform, the wave equation with a mean flow can be reduced to the ordinary equation. Allowance is also made in the analysis for the case of a swept wing. The same combination of Galilean and Lorentz transforms lead to a problem with no flow but a different sweep. The solution procedures for the cases of leading and trailing edges are basically the same. Two normalizations of the solution are given by the computer program. FORTRAN computer programs are presented with detailed documentation. The output from these programs compares favorably with the results of other investigators.

Amiet, R. K.↗
DOE OSTI2015

Relativistic nuclear theory—nucleons and mesons: origin, current status, and trends

The nuclear shell model (NSM) is a fundamental model of nuclear theory. At the initial stage, the NSM was developed on the basis of the Schrödinger equation, in particular because it was not clear which Dirac matrices should be associated with various components of the (relativistic) shell model potential. In the early 1970s, the relativistic version of the NSM with meson fields as its main components was developed on the basis of the Dirac equation. The relativistic nuclear shell model (RNSM) includes meson fields with different space–time transformation properties (scalar, four-vector, etc.) that determine the behavior of the (corresponding) meson fields under Lorentz transformations. This fact directly indicates that nuclear theory should be relativistic and based on the Dirac equation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1966

Lectures on Relativity Theory

Relativity theory lectures involving Lorentz transformations, Minkowski space, and tensor analysis

RELATIVITY THEORY↗