The Pauli-Lubanski Vector and Photon Helicity (original) (raw)
arXiv: Quantum Physics, 2017
Einstein's photo-electric effect allows us to regard electromagnetic waves as massless particles. Then, how is the photon helicity translated into the electric and magnetic fields perpendicular to the direction of propagation? This is an issue of the internal space-time symmetries defined by Wigner's little group for massless particles. It is noted that there are three generators for the rotation group defining the spin of a particle at rest. The closed set of commutation relations is a direct consequence of Heisenberg's uncertainty relations. The rotation group can be generated by three two-by-two Pauli matrices for spin-half particles. This group of two-by-two matrices is called SU(2), with two-component spinors. The direct product of two spinors leads to four states leading to one spin-0 state and one spin-1 state with three sub-states. The SU(2) group can be expanded to another group of two-by-two matrices called SL(2,c), which serves as the covering group for the gr...
A Note on the Lorentz Transformations for the Photon
Foundations of Physics Letters, 2006
We discuss transormation laws of electric and magnetic fields under Lorentz transformations, deduced from the Classical Field Theory. It is found that we can connect the resulting expression for a bivector formed with those fields, with the expression deduced from the Wigner transformation rules for spin-1 functions of massive particles. This mass parameter should be interpreted because the constancy of speed of light forbids the existence of the photon mass.
Self/anti-self charge conjugate states in the helicity basis
2013
We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2, 0) ⊕ (0, 1/2) representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problem of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (P, C, T) are studied. Particular attention has been paid to the question of (anti)commutation of the Charge conjugation operator and the Parity in the helicity basis. Dynamical equations have also been presented. In the (1/2, 0) ⊕ (0, 1/2) representation they obey the Dirac-like equation with eight components, which has been first introduced by Markov. Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino). The chirality and the helicity (two concepts which are frequently confused in the literature) for Dirac and Majorana states have been discussed.
The helicity amplitude approach to low energy theorems
Annals of Physics, 1973
It is shown that "low energy theorems" for charged vector and axial vector currents have a natural derivation in terms of helicity amplitudes. This is done by reconsidering the kinematic constraints as a function of the virtual photon mass, A. The crucial point is that in general a certain limit of the longitudinal amplitudes is required as an input to the theorem. Two new YV sum rules are also obtained.
Revisiting fermion helicity flip in Podolsky's Electromagnetism
arXiv: High Energy Physics - Phenomenology, 2016
The spin projection of a massive particle onto its direction of motion is called helicity (or "handedness"). It can therefore be positive or negative. When a particle's helicity changes from positive to negative (or vice-versa) due to its interaction with other particles or fields, we say there is a helicity flip. In this work we show that such helicity flip can be seen for an electron of 20MeV20 MeV20MeV of energy interacting with a charged scalar meson through the exchange of a virtual photon. This photon {\it does not} necessarily need to be Podolsky's proposed photon; in fact, it is independent of it.
Optical Helicity and Chirality: Conservation and Sources
Applied Sciences
We consider the helicity and chirality of the free electromagnetic field, and advocate the former as a means of characterising the interaction of chiral light with matter. This is in view of the intuitive quantum form of the helicity density operator, and of the dual symmetry transformation generated by its conservation. We go on to review the form of the helicity density and its associated continuity equation in free space, in the presence of local currents and charges, and upon interaction with bulk media, leading to characterisation of both microscopic and macroscopic sources of helicity.
Dual electromagnetism: Helicity, spin, momentum, and angular momentum
2012
The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy-momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dualsymmetric Lagrangian formulation of classical electromagnetism. This dual electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy-momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches.
Unified formulation for helicity and continuous spin fermionic fields
Journal of High Energy Physics
We propose a unified BRST formulation of general massless fermionic fields of arbitrary mixed-symmetry type in d-dimensional Minkowski space. Depending on the value of the real parameter the system describes either helicity fields or continuous spin fields. Starting with the unified formulation we derive a number of equivalent descriptions including the triplet formulation, Fang-Fronsdal-Labastida formulation, light-cone formulation and discuss the unfolded formulation.
On the Photon Vertex and Half-Integer Spin
2023
When rewriting the photon vertex of quantum electrodynamics in terms of geometrical quantities, various elements can be mapped directly to objects and properties known from classical projective geometry (PG). Elements of P5 when mapped to line reps in P3 exhibit their intrinsic Lorentz invariance associated to automorphisms of the Plücker-Klein quadric M42{M}_{4}^{2}M42, and line reps when expressed by point or plane coordinates introduce (one-parameter) pencils, or formally gl(2,${\bf R}$), or gl(1,${\bf H$}) which covers su(2)⊕u(1). This introduces binary forms and, using a potential approach of central forces, Schrödinger or Laplace equations and the respective special functions, as well as the projective generation of quadrics like in Dirac's approach which legitimates Clifford algebra elements as linear factors in invariant theory and the quadratic algebra to represent geometry. Physically, this identification allows for the classical concept of moments in terms of tetrahedrons which on the one hand relates to previous work on SU(4) and SU*(4) in quantum representations. On the other hand, it relates to the classical physical definitions, however, exhibiting a factor 2 between contemporary (euclidean) moments and the tetrahedral construction used in the vertex. Finally, we discuss the equilibrium conditions with respect to gauge and Yang-Mills theories in general as well as the related objects and their transformation theory.
Matrix Approach to Helicity States of Dirac Free Particles
arXiv (Cornell University), 2022
We use elementary matrix algebra to derive the free wave solutions of the Dirac equation and examine the fundamental concepts of spin, polarization, and helicity states in details. This consideration can aid readers in studying the mathematical methods of relativistic quantum mechanics. Could anything at first sight seem more impractical than a body which is so small that its mass is an insignificant fraction of the mass of an atom of hydrogen? Comment on the electron by J. J. Thomson, Nobel Prize in Physics 1906 [21] I studied mathematics with passion because I considered it necessary for the study of physics, to which I want to dedicate myself exclusively.