Simplified derivation of the crossing relations using the substitution rule as a guide

1979 ◽  
Vol 57 (5) ◽  
pp. 706-716
Author(s):  
Richard A. Morrow
Keyword(s):  
Analytic Continuation ◽  
Weak Interaction ◽  
Rest Frame ◽  
Center Of Mass ◽  
Lorentz Transformations ◽  
Simple Derivation ◽  
Wigner Rotation ◽  
Substitution Rule ◽  
Rotation Matrices ◽  
Helicity Amplitudes

A simple derivation of the Trueman–Wick crossing relations for center of mass helicity amplitudes is presented. The method uses only Wigner rotation matrices and does not deal specifically with more general Lorentz transformations. Each particle is treated individually in turn in its own rest frame in order to discover how its helicity transforms under crossing and the substitution rule is used as a guide in determining the outcome of the analytic continuation. Crossing relations for different paths of analytic continuation in the s–t plane are discussed and it is shown that care must be exercised when dealing with weak interaction amplitudes. The method presented may be extended straightforwardly to multiparticle amplitudes.

scholarly journals SPIN–MOMENTUM CORRELATION IN RELATIVISTIC SINGLE-PARTICLE QUANTUM STATES

2010 ◽  
Vol 08 (03) ◽  
pp. 517-528 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
M. MAHDIAN
Keyword(s):  
Single Particle ◽  
Inertial Frame ◽  
Quantum States ◽  
Moving Frame ◽  
Lorentz Transformations ◽  
Mixed States ◽  
Wigner Rotation ◽  
Lorentz Boost ◽  
Momentum Correlation ◽  
Spin Momentum

This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.

HELICITY AMPLITUDES FOR COLLIDING BEAM SCATTERING OF TWO SPIN 1/2 PARTICLES

1993 ◽  
Vol 08 (30) ◽  
pp. 5383-5407
Author(s):  
T.B. ANDERS ◽  
A.O. BARUT ◽  
W. JACHMANN
Keyword(s):  
Center Of Mass ◽  
Mass System ◽  
Intermediate Transformation ◽  
Beam System ◽  
Pair Annihilation ◽  
Helicity Amplitudes ◽  
Reaction Channels ◽  
Invariant Coupling ◽  
Exchange Scattering ◽  
The One

As a generalization and extension of the extensive tables of polarization asymmetries given in a previous work,1 we present here tables of helicity amplitudes for the scattering of two spin 1/2 particles in the colliding beam system (i.e. two incoming particles with opposite directions but not necessarily of equal momenta). The particles belonging to the same current may have different masses in order to describe particle excitations. The amplitudes are given for six different basic couplings connecting two vector vertices, a vector vertex at the one current and a derivative vector vertex at the other current, two derivative vector vertices, two tensor vertices, and two scalar vertices. The vertices include axial couplings by factors of type 1+cγ5. The amplitudes are written as expressions with 16 components in the six different reaction channels, namely the scattering of two fermions, of two antifermions, and of a fermion and an antifermion, the pair creation by pair annihilation, as well as the exchange scattering for two identical fermions or antifermions. The formulas may be used for an analysis which extracts the invariant coupling functions from the experimental data obtained in the colliding beam system directly without an intermediate transformation to the center of mass system.

Lorentz Transformation as a Galilei Transformation with Physical Length and Time Contractions

1988 ◽  
Vol 43 (10) ◽  
pp. 859-864
Author(s):  
H. E. Wilhelm
Keyword(s):  
Rest Frame ◽  
Lorentz Transformations ◽  
Speed Of Light ◽  
Analogous Structure ◽  
Galilean Relativity ◽  
Symmetry Properties ◽  
Inertial Frames ◽  
Ether Frame ◽  
Light Signals ◽  
Time Variables

Abstract The Lorentz transformations between the space-time coordinates of a point in two inertial frames with arbitrary relative velocity, are reformulated as Galilei transformations with length and time contractions, by introducing the ether rest frame (in which light signals propagate isotropically with the vacuum speed of light). The generalized Galilei transformations for the (longitudinal) space coordinates (x1,2) and the time variables (t1,2) of a point in two inertial frames ∑1,2 are not only of analogous structure, but have remarkable symmetry properties, too. The appearing length and time contractions are absolute effects in the sense of Lorentz-Fitzgerald, i.e., a rod has its largest length and a clock its fastest rate when at rest in the ether frame ∑0. Thus, an analytical reformulation and a physical interpretation of the Lorentz transformations within Galilean relativity physics is achieved.

scholarly journals GENERALIZED EULERIAN COORDINATES FOR RELATIVISTIC FLUIDS: HAMILTONIAN REST-FRAME INSTANT FORM, RELATIVE VARIABLES, ROTATIONAL KINEMATICS

2004 ◽  
Vol 19 (17n18) ◽  
pp. 3025-3082 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Rest Frame ◽  
Deformable Body ◽  
Center Of Mass ◽  
Relativistic Fluids ◽  
Instant Form ◽  
Perfect Fluids ◽  
Rotational Kinematics ◽  
Eulerian Coordinates ◽  
New Formulation

We study the rest-frame instant form of a new formulation of relativistic perfect fluids in terms of new generalized Eulerian configuration coordinates. After the separation of the relativistic center of mass from the relative variables on the Wigner hyper-planes, we define orientational and shape variables for the fluid, viewed as a relativistic extended deformable body, by introducing dynamical body frames. Finally we define Dixon's multipoles for the fluid.

Lorentz Invariance of Entanglement

2002 ◽  
Vol 2 (6) ◽  
pp. 487-512
Author(s):  
P.M. Alsing ◽  
G. Milburn
Keyword(s):  
Lorentz Invariance ◽  
Bell States ◽  
Explicit Calculation ◽  
Particle State ◽  
Lorentz Transformations ◽  
Wigner Rotation ◽  
Bipartite State ◽  
Relativistic Analog ◽  
Massive Spin ◽  
Inertial Frames

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin $1/2$ particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

scholarly journals DARK ENERGY IN MOTION

2006 ◽  
Vol 15 (12) ◽  
pp. 2165-2170 ◽  
Author(s):  
ANTONIO L. MAROTO
Keyword(s):  
Dark Energy ◽  
Large Scale ◽  
Rest Frame ◽  
Background Radiation ◽  
Center Of Mass ◽  
Usual Definition ◽  
Peculiar Velocity ◽  
Cosmological Principle ◽  
Definition Of

Recent large-scale peculiar velocity surveys suggest that large matter volumes could be moving with appreciable velocity with respect to the CMB rest frame. If confirmed, such results could conflict with the Cosmological Principle according to which the matter and CMB rest frames should converge on very large scales. In this work, we explore the possibility that such large-scale bulk flows are due, not to the motion of matter with respect to the CMB, but to the flow of dark energy with respect to matter. Indeed, when dark energy is moving, the usual definition of the CMB rest frame as that in which the CMB dipole vanishes is not appropriate. We find instead that the dipole vanishes for observers at rest with respect to the cosmic center of mass, i.e. in motion with respect to the background radiation.

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