Sophie Chabysheva

• at U Idaho
  • Phys 371 Mathematical Physics
  • Phys 341 Electromagnetic Fields I
  • Phys 342 Electromagnetic Fields II
  • Phys 213 Engineering Physics III
• at UM-Duluth
  • Phys 5521 Quantum Mechanics I
  • Phys 5511 Electrodynamics
  • Phys 4021 Quantum Physics II
  • Phys 4011 Electromagnetic Theory
  • Phys 4001 Classical Mechanics
  • Phys 2013 General Physics I discussion
  • Phys 2015 General Physics II discussion
  • Math 3298 Calculus III
  • Math 1296 Calculus I

Quantum field theories are used to describe interactions between fundamental particles. The Standard Model of particle physics is essentially a collection of such theories that attempt to describe nature at a very basic level. This Model has been quite successful; however, a complete understanding of strongly interacting matter, such as atomic nuclei, remains elusive. High-energy scattering processes are relatively well understood, because matter is then weakly coupled, and experiments have provided convincing evidence that the correct theory of strong nuclear interactions is a nonlinear generalization of electromagnetism called quantum chromodynamics (QCD). The fundamental building blocks of QCD are quarks and gluons, which are bound together into hadrons, such as protons, neutrons, and pions, and which are in turn bound into atomic nuclei. The process of these bindings, and the properties of hadrons in general, which should be derivable from QCD, are not yet understood. This project is a continuation of an effort to develop methods to reach such an understanding and to eventually compute hadron properties from QCD.

The methods are based on Dirac's light-front coordinates, where time evolves along a light wave front, and on a Hamiltonian formulation of quantum field theories. [For reviews, see S.J. Brodsky, H.-C. Pauli, and S.S. Pinsky, Phys. Rep. 301, 299 (1998) and J.R. Hiller, Prog. Part. Nucl. Phys. 90, 75 (2016).] The coordinates allow a nearly nonrelativistic description of dynamics and a construction of hadronic states in terms of wave functions for the constituent quarks and gluons. This admits an intuitive interpretation of hadrons in terms of ordinary quantum mechanics, in contrast to lattice gauge theory, where wave functions are not available. The state of the system is expanded in a basis of momentum eigenstates, with wave functions as the coefficients in the expansion. The wave functions satisfy an infinite coupled system of integral equations, which is usually solved by first truncating to a finite subset. However, the truncation can cause problems with the cancellation of infinities that arise in individual terms. A new method, the light-front coupled-cluster (LFCC) method [S.S. Chabysheva and J.R. Hiller, Phys. Lett. B 711, 417 (2012)]. has been recently developed to avoid explicit truncation of the equations and instead represent the infinite set of wave functions by a finite set of auxiliary functions.

Another important step has been the development of a regularization scheme for nonperturbative calculations in light-front QCD. [S.S. Chabysheva and J.R. Hiller, arXiv: 1506.05429.] This extends earlier work on covariant-gauge light-front QED [S.S. Chabysheva and J.R. Hiller, Phys Rev D 84, 034001 (2011)] to non-Abelian gauge theories. The scheme is based on the introduction of Pauli--Villars (PV) quarks and gluons to the QCD Lagrangian in such a way that the full Lagrangian is invariant with respect to off-shell BRST transformations of the fields in an arbitrary covariant gauge. This requires an extension of the underlying gauge symmetry and additional scalar and ghost fields. The scalars provide masses for the PV gluons and split the mass degeneracy of the PV quarks through a non-Abelian Stueckelberg mechanism. The regularization is arranged by having all interaction terms in the Lagrangian be couplings between null fields, specific combinations of positive and negative-metric PV fields. In the infinite-PV-mass limit, the original Lagrangian is restored.

One current project is an investigation of the convergence of the LFCC method with respect to the number and structure of the auxiliary functions. This is being done in the context of a relatively simple quantum field theory, the so-called quenched scalar Yukawa model [Y.~Li, V.~A.~Karmanov, P.~Maris, and J.~P.~Vary, Phys. Lett. B 748, 278 (2015).] The model has two particle types, one charged and one neutral, and only one type of interaction: emission and absorption of a neutral by a charged particle. The ``charge'' is just a conserved quantum number and not an electrical charge. The quenched model explicitly excludes pair production and annihilation, which would, in fact, make the theory unstable. Each charged particle can ``dress'' itself with a cloud of neutrals and can interact with another charged particle by exchange of neutrals.