Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1509.00431

Interpolating Helicity Spinors Between the Instant Form and the Light-front Form

Ziyue Li·Murat An·Chueng-Ryong Ji
View original source ↗Read source document ↗Export metadata ↓

Abstract

We discuss the helicity spinors interpolating between the instant form dynamics (IFD) and the front form dynamics, or the light-front dynamics (LFD), and present the interpolating helicity amplitudes as well as their squares for the scattering of two fermions, and the annihilation of fermion and anti-fermion. We parametrize the interpolation between the two dynamics, IFD and LFD, by an interpolation angle and derive not only the generalized helicity spinors in the $(0,J)\oplus(J,0)$ chiral representation that links naturally the two typical IFD vs. LFD helicity spinors but also the generalized Melosh transformation that relates these generalized helicity spinors to the usual Dirac spinors. Analyzing the directions of the particle momentum and spin with the variation of the interpolation angle, we inspect the whole landscape of the generalized helicity intermediating between the usual Jacob-Wick helicity in the IFD and the light-front helicity in the LFD. Our analysis clarifies the characteristic difference of the helicity amplitudes between the IFD and the LFD. In particular, we find that the behavior of the angle between the momentum direction and the spin direction bifurcates at a critical interpolation angle and the IFD and the LFD separately belong to the two different branches bifurcated at this critical interpolation angle. This finding further clarifies any conceivable confusion in the prevailing notion of the equivalence between the infinite momentum frame and the LFD. The existence of the universal J-curve found in our previous works of scalar field theory and the sQED theory is confirmed in the present work of interpolating helicity amplitudes for the fermion scattering and annihilation processes. In conjunction with the bifurcation of branches, the two boundaries appear in the interpolating helicity amplitudes and interestingly the J-curve persists within these two boundaries.

Explore related subjects

hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ziyue Li, Murat An, Chueng-Ryong Ji. 2015-09-01. Interpolating Helicity Spinors Between the Instant Form and the Light-front Form. https://doi.org/10.1103/physrevd.92.105014

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization

We investigate timelike entanglement in quantum field theory using spacetime density matrices and provide a microscopic lattice realization. For a two-dimensional free real scalar field, we extend Gaussian diagonalization methods to the generally non-Hermitian reduced spacetime density matrix and determine its complete nonzero spectrum in the generic regular case, together with all integer R\'enyi moments. The real-time replica construction identifies these moments with Lorentzian branch-point twist-operator correlation functions. We test this identification against the full four-point function on a circle, boundary two-point functions with Dirichlet and Neumann boundary conditions, and massive form-factor predictions, finding quantitative agreement in both magnitude and phase across distinct causal regimes. The boundary setup exhibits a finite causally connected window in which every integer R\'enyi entropy is real, showing that reality is not equivalent to causal disconnection. These results provide a microscopic lattice foundation for timelike entanglement and for Lorentzian twist-operator methods beyond equal-time regions.

hep-th↗
arXiv2026

Landau-Ginzburg description of an exceptional ${\mathcal N}=1$ minimal model

The $\mathcal N=1$ superconformal minimal model with $m=12$ and the exceptional modular invariant $(E_6,D_8)$ is the unitary minimal model of the super-$W_3$ algebra. We propose its Landau-Ginzburg description using two real scalar superfields with the cubic superpotential ${\cal W}=g_1 XY^2/2 + g_2X^3/6$. For $g_1=g_2$, this superpotential is known to describe a product of two $m=3$ $\mathcal N=1$ superconformal minimal models, which is the $m=10$ model with the $(D_6,E_6)$ modular invariant. The exceptional $m=12$ superconformal minimal model is realized at a different fixed point of the same theory. Testing this Landau-Ginzburg description requires the fusion ring of the minimal model, which we obtain from the modular data of the extended algebra. The fusion ring has a $\mathbb Z_2$ grading by chiral fermion parity that the ordinary fusion coefficients do not determine. This grading, composed with conjugation, gives the generator of the R-parity $\mathbb Z_2^{R}$ of the Landau-Ginzburg theory. We then treat the theory with superpotential $\cal W$ as a Gross-Neveu-Yukawa model in $d=4-\epsilon$ and find a weakly coupled infrared fixed point with $g_1/g_2=3/2+\mathcal O(\epsilon)$, at which supersymmetry emerges. We also describe the renormalization group flow from this fixed point to the decoupled fixed point with $g_1=g_2$. The operator dimensions at the coupled fixed point, continued to $d=2$, agree approximately with their values in the $m=12$ superconformal minimal model. Finally, we estimate the scaling dimensions in the new interacting $d=3$ $\mathcal N=1$ superconformal field theory.

hep-th↗
arXiv2026

Detecting one-dimensional bosonic SPT phases via twisted entropic order parameter

Entanglement asymmetry, introduced by F. Ares, S. Murciano and P. Calabrese, provides a density-matrix diagnostic of symmetry breaking and successfully captures the Landau data associated with a broken symmetry pattern. However, it is by now well established that gapped quantum many-body systems can exhibit phases which are not characterized solely by Landau symmetry breaking. A fundamental example is a symmetry-protected topological (SPT) phase, and the ordinary definition of entanglement asymmetry is insensitive to this topological information. In this work we introduce a refined quantity, which we call the twisted entropic order parameter, designed to detect SPT phases from reduced density matrices, particularly focusing on one-dimensional bosonic systems. The key ingredient in our construction is an ancilla degrees of freedom that coherently records the untwisted state and the twisted state associated to a one-ended topological defect of unbroken symmetry, so that the enlarged density matrix retains the charge carried by the defect endpoint. We demonstrate our proposal in concrete lattice models and further generalize it beyond ordinary group symmetries, establishing its ability to diagnose SPT phases. This provides a first step toward a unified entanglement-asymmetry framework for diagnosing quantum phases of matter.

hep-th↗