Yang Li

Professor in Physics
University of Science and Technology of China



Non-Perturbative QCD, Hadronic Physics and Computational Physics

The High-Energy Nuclear Theory Group

What's new

2023-2024 ILCAC Seminars (third Wednesdays, 13:30 GMT/21:30 BJT). This seminar series focuses on physics of strongly interacting particles and related issues.

2023-2024 LFQCD Seminars (first Wednesday, 13:00 GMT/21:00 BJT). This seminar series is a platform for early-career researchers to present their recent work and to exchange ideas on non-perturbative aspects of QCD, especially on light-front QCD and hadron structures.

Teaching & Advising



  • Fall 2021, Mechanics A
  • Fall 2020, Group Theory
  • Spring 2016, Introduction to Classical Physics I (Rec & Lab)
  • Fall 2012, Introduction to Classical Physics I (Rec)
  • Fall 2011, General Physics (Rec)
  • Fall 2011, Introduction to Modern Physics I
  • Spring 2011, Introduction to Classical Physics I (Lab)
  • Fall 2010, General Physics (Lab)
  • Fall 2010, Physics for the Nonscientist

Advising & Mentorship

  • Yihan Duan, Non-perturbative light-cone Hamiltonian approach to parton distributions, undergraduate thesis, 2023 Spring, University of Science and Technology of China (Outstanding Thesis)
  • Zhiguo Wang, Radiative decay of charmonium vector meson, undergraduate thesis, 2022 Spring, Lanzhou University
  • Xianghui Cao, Relativistic bound states of scalar field theory on the light cone, undergraduate thesis, 2022 Spring, University of Science and Technology of China (Outstanding Thesis)
  • Jialin Chen, 基函数光前量子化方法研究奇异介子, undergraduate thesis, 2021 Spring, Lanzhou University
  • Wenyang Qian, Relativistic bound states within Basis Light-Front Quantization, Ph.D. thesis, 2020, Iowa State University (Present affiliation: Postdoc at Iowa State University)
  • Shuo Tang, Relativistic bound states on the light front, Ph.D. thesis, 2020, Iowa State University (Present affiliation: )
  • Anji Yu, Baryons in a light front approach, graduate thesis, 2019, Iowa State University (Present affiliation: Software Engineer at Google Inc.)
  • Meijian Li, Non-perturbative applications of quantum chromodynamics, Ph.D. thesis, 2019, Iowa State University (Present affiliation: Postdoc at University of Santiago de Compostela, Spain)
Topical discussions


My recent research focuses on high-energy theory, in particular, the non-perturbative QCD, hadron structure and computational physics. You can check out my published work, recent talks and developements.

Here are some information for beginners.

Physical background

The quantum chromodynamics (QCD) describes the interactions between quarks and gluons. It is strong coupling at low-enegy scale, which leads to remarkable non-perturbative physics, e.g. confinement and chiral symmetry breaking. \[ \mathscr L_{\text{QCD}} = \overline\psi \big(i\gamma^\mu D_\mu-m\big)\psi - \frac{1}{4} F_{\mu\nu c}F^{\mu\nu c} \] The non-perturbative calculation of QCD is one of the most formidable challenges in physics. It is also the key to answer some of the fundamental questions in Nuclear Physics, such as how the quarks and gluons are binding together, and how the nuclear forces are formed to bind the nucleons. The non-perturbative properties of hadrons is also the focii of some present and forthcoming high-energy experiments, such as the 12 GeV upgrade of CEBAF at Jefferson Lab, the electron-ion collider (eRHIC) at Brookheaven National Lab, both in United States, the LHCb & ALICE experiments at CERN in Europe, the electron ion collider of China (EicC) at HIAF in Huizhou, the BESIII experiment at BEPC in Beijing, as well as the Belle II experiment at KEK in Japan.

The Hamiltonian formalism is one of the fundamental theoretical frameworks of quantum theory and is widely used in physics. This formulation is non-perturbative and provides access to information at the amplitude level as well as the real-time evolution information, through the Schrödinger equation. The Hamiltonian formalism has been a standard tool in addressing strong coupling quantum many-body systems, such as the nuclei, atoms as well as the molecules. \[ i\frac{\partial}{\partial x^+}|\psi(x^+)\rangle = P_+|\psi(x^+)\rangle \] The light-front dynamics, proposed by Paul Dirac, exploits dynamical evolution in the light-front time \(x^+ = t + z/c\). It brings several dramatic simplification to the relativistic dynamics. Thus the light-front Hamiltonian formalism is a natural framework for describing hadrons as relativistic bound states. It is non-perturbative and provides direct access to the hadronic observables in Richard Feynman's parton picture, one of the modern pillars in high-energy scattering experiments.

Recent advances in computational sciences (including quantum computing) provide opportunities to compute the non-perturbative solutions of QCD from first principles. Of course, the unique challenges posed by QCD require significant efforts in both the computational front and the physical front, separately and joinly, which are what I try to address in my research.

Basis light-front quantization

Basis light-front quantization (BLFQ) is a numerical framework to solve light-front QCD as quantum many-body problems. It is inspired by the recent development in ab initio nuclear structure calculations. BLFQ is designed to preserve all kinematically symmetries of the Hamiltonian and exploits the sparse matrix technologies to accelerate the quantum many-body calculations.

\[ H_\text{eff} = \sum_i \frac{\vec p_{i\perp}^2+m_i^2}{x_i} + U_i + \sum_{i,j} V_{ij}^{(2)} + \cdots + V^{(a)} + H_\text{cm} \] The starting point of BLFQ is an effective Hamiltonian defined in a designated model space. To obtain the effective Hamiltonian, one can start from the canonical QCD Hamiltonian at high-energy scales and obtain the bound-state effective Hamiltonian from the Hamiltonian renormalization group method, as is demonstrated in quantum electrodynamics (QED).

Alternatively, one can employ phenomenological effective interactions at low-energy scale. We proposed a model based on confining interactions from light-front holography and a one-gluon exchange interaction. We use the model to investigate the meson spectroscopy. The obtained light-front wave functions can be used to access hadronic observables and parton distributions.

Fock sector dependent renormalization

Non-perturbative renormalization is one of the fundamental challenges in quantum field theory (QFT) at strong coupling. The challenge is amplified in the Hamiltonian formulation of QFT, as explicit covariance is lost there. Remarkably, cluster decomposition still holds in light-front dynamics, even though all diagrams are strictly light-front time ordered. This fact is exploited in the Fock sector dependent renormalization (FSDR) to enable non-perturbative renormalization in light-front field theories with systematic Fock sector truncations. FSDR has been successfully applied to (3+1)d QFTs, including scalar Yukawa theory, Yukawa theory and QED, with exact cancellations of ultraviolet divergences. The scalar Yukawa theory in particular is computed up to a Fock sector of 3 dressing particles and a good Fock sector convergence is achieved for form factors.

Hadron spectrum and structures

We developed a relativistic model for hadrons based on light-front holography and light-front QCD. With a few phenomenological parameters, the model is able to produce hadron spectrum and observables comparable to the experimental measurements. With the obtained light-front wave functions, it provides the direct access to parton distributions that describe the 3D structure of the hadrons. The model is successfully applied to quarkonium, heavy-light systems, light mesons and nucleons with mixed success. It is the one of few models that provide a unified description of hadron spectra and structures.

Chiral symmetry breaking and the pion

Pion is the lightest hadron. It consists of a quark and an antiquark. However, its mass \(M_\pi\) = 140 MeV is much lighter than the mass of the constituent quarks \(m_q \approx M_p/3\) = 320 MeV. It is believed to be an elementary Nambu-Goldstone boson of the spontaneously broken chiral symmetry. One of the curious questions is what is the structure of the pion to accommodate both the physics of chiral symmetry breaking and confinement. We derived an exact relation (called a sum rule) for the pion wave function based on the axial-vector current conservation and the general covariant structure of the light front wave functions. This sum rule suggests that confinement and chiral symmetry breaking dictate the long-distance and short-distance parts of the wave function, respectively. As such, the effective quark-antiquark potential must be in the shape of a sombrero (Mexican hat). Taking advantage of the light-front holography, we further show that the chiral sum rule is consistent with the chiral symmetry breaking in AdS/QCD through the Higgs mechanism. Finally, these findings lead to a striking 3D picture of the pion: it is a uniform disk in the transverse direction and infinitely long in the longitudinal direction.

Other interests

  • QCD at finite temperature
  • Quantum many-body theory & quantum computing
  • Low-energy nuclear physics
  • Advanced algorithms in computational physics
  • Foundations of quantum mechanics



List of publications

  1. Yihan Duan, Siqi Xu, Shan Cheng, Xingbo Zhao, Yang Li, James P. Vary, Flavor asymmetry from the non-perturbative nucleon sea, [arXiv: 2404.07755 [hep-ph]]
  2. Siqi Xu, Xianghui Cao, Tianyang Hu, Yang Li, Xingbo Zhao, James P. Vary, Stress out of charmonia, [arXiv: 2404.06259 [hep-ph]]
  3. Yang Li, James Vary, Stress inside the pion in holographic light-front QCD, Phys. Rev. D 109, L051501 (2024); [arXiv:2312.02543 [hep-th]]
  4. Zhiguo Wang, Meijian Li, Yang Li, James P. Vary, Shedding light on charmonium, Phys. Rev. D 109, L031902 (2024); [arXiv:2312.02604 [hep-ph]]
  5. Siqi Xu, Chandan Mondal, Xingbo Zhao, Yang Li and James P. Vary, Quark and gluon spin and orbital angular momentum in the proton, Phys. Rev. D 108, 094002 (2023)
  6. Xianghui Cao, Yang Li, James Vary, Forces inside a strongly-coupled scalar nucleon, Phys. Rev. D 108, 056026 (2023); [arXiv: 2308.06812 [hep-ph]]
  7. James Vary, Yang Li, Chandan Mondal, Xingbo Zhao, Light-front quantization, in 50 Years of Quantum Chromodynamics, Eds. Franz Gross and Eberhard Klempt, Eur. J. Phys. C 83, 1125 (2023); [arXiv: 2209.08584 [hep-ph]]
  8. Siqi Xu, Chandan Mondal, Xingbo Zhao, Yang Li, James P. Vary, Nucleon spin decomposition with one dynamical gluon, [arXiv: 2209.08584 [hep-ph]]
  9. Yang Li, Wen-bo Dong, Yi-liang Yin, Qun Wang, James P. Vary, Minkowski's lost legacy and hadron electromagnetism, Phys. Lett. B 838 (2023) 137676; [arXiv: 2206.12903 [hep-ph]]
  10. Yang Li, P. Maris, and J.P. Vary, Chiral sum rule on the light front, Phys. Lett. B 836 (2023) 137598; [arXiv: 2203.14447 [hep-th]]
  11. Yang Li, and J.P. Vary, Longitudinal dynamics for mesons on the light cone, Phys. Rev. D 105, 114006 (2022); [arXiv: 2202.05581 [hep-ph]]
  12. Yang Li, Meijian Li, and J.P. Vary, Two-photon transitions of charmonia on the light front, Phys. Rev. D 105 (2022) 7, L071901; [arXiv: 2111.14178 [hep-ph]]
  13. Meijian Li, Yang Li, Guangyao Chen, T. Lappi, and J.P. Vary, Light-front wavefunctions of mesons by design, Eur. Phys. J. C 82 (2022) 11; [arXiv: 2111.07087 [hep-ph]]
  14. Siqi Xu et al. (BLFQ Collaboration), Nucleon structure from basis light-front quantization, Phys. Rev. D 104 (2021) 9, 094036; [arXiv: 2108.03909 [hep-ph]]
  15. Yang Li, and J.P. Vary, Light-front holography with chiral symmetry breaking, Phys. Lett. B 825 (2022) 136860; [arXiv:2103.09993 [hep-ph]]
  16. W. Qian, S. Jia, Yang Li, and J.P. Vary, Light mesons within the basis light-front quantization framework, Phys. Rev. C 102, no.5, 055207 (2020); [arXiv:2005.13806 [nucl-th]].
  17. M. Li, X. Zhao, P. Maris, G. Chen, Yang Li, K. Tuchin and J.P. Vary, Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach, Phys. Rev. D 101, no.7, 076016 (2020); [arXiv:2002.09757 [nucl-th]].
  18. S. Tang, Yang Li, P. Maris and J. P. Vary, Heavy-light mesons on the light front, Eur. Phys. J. C 80, no.6, 522 (2020); [arXiv:1912.02088 [nucl-th]].
  19. J. Lan, C. Mondal, M. Li, Yang Li, S. Tang, X. Zhao and J.P. Vary, Parton Distribution Functions of Heavy Mesons on the Light Front, Phys. Rev. D 102, no.1, 014020 (2020); [arXiv:1911.11676 [nucl-th]].
  20. W. Du, Yang Li, X. Zhao, G.A. Miller and J.P. Vary, Basis Light-Front Quantization for a Chiral Nucleon-Pion Lagrangian, Phys. Rev. C 101, no.3, 035202 (2020); [arXiv:1911.10762 [nucl-th]].
  21. C. Mondal, S. Xu, J. Lan, X. Zhao, Yang Li, D. Chakrabarti and J.P. Vary, Proton structure from a light-front Hamiltonian, Phys. Rev. D 102, no.1, 016008 (2020); [arXiv:1911.10913 [hep-ph]].
  22. M. Li, Yang Li, P.Maris and J.P. Vary, Frame dependence of transition form factors in light-front dynamics, Phys. Rev. D 100, no.3, 036006 (2019); [arXiv:1906.07306 [nucl-th]].
  23. G. Chen, Yang Li, K. Tuchin, and J.P. Vary, Heavy quarkonia production at energies available at the CERN Large Hadron Collider and future electron-ion colliding facilities using basis light-front quantization wave functions, Phys. Rev. C 100, no.2, 025208 (2019); [arXiv:1811.01782 [nucl-th]].
  24. L. Adhikari, Yang Li, M.-j. Li, P. Maris, J.P. Vary, Form factors and generalized parton distributions of heavy quarkonia in basis light front quantization, Phys. Rev. C 99, no.3, 035208 (2019); [arXiv:1809.06475 [hep-ph]].
  25. S. Tang, Yang Li, P. Maris, J.P. Vary, Bc mesons and their properties on the light front, Phys. Rev. D 98, no.11, 114038 (2018); [arXiv:1810.05971 [nucl-th]]
  26. M.-j. Li, Yang Li, P. Maris, and J.P. Vary, Radiative transitions between 0-+ and 1-- heavy quarkonia on the light front, Phys. Rev. D 98, 034024 (2018); [arXiv:1803.11519 [hep-ph]]
  27. Weijie Du, Peng Yin, Yang Li, Guangyao Chen, Wei Zuo, Xingbo Zhao, James P. Vary, Coulomb Excitation of Deuteron in Peripheral Collisions with a Heavy Ion, Phys. Rev. C 97, 064620 (2018); [arXiv:1804.01156 [nucl-th]]
  28. Yang Li, P. Maris and J.P. Vary, Frame dependence of form factors in light-front dynamics, Phys. Rev. D 97, 054034 (2018); [arXiv:1712.03467 [hep-ph]]
  29. Yang Li, Kirill Tuchin, Electrodynamics of dual superconducting chiral medium, Phys. Lett. B 776, 270 (2018); [arXiv:1708.08536 [hep-ph]]
  30. S. Leitão, Yang Li, P. Maris, M.T. Peña, A. Stadler, J.P. Vary, E.P. Biernat, Comparison of two Minkowski-space approaches to heavy quarkonia, Eur. J. Phys. C, 66, 696 (2017); [arXiv:1705.06178 [hep-ph]]
  31. Yang Li, P. Maris, J.P. Vary, Quarkonium as relativistic bound state on the light front, Phys. Rev. D 96, 016022 (2017); [arXiv:1704.06968 [hep-ph]]
  32. G. Chen, X. Zhao, Yang Li, K. Tuchin and J.P. Vary, Particle distribution in intense fields in a light-front Hamiltonian approach, Phys. Rev. D 95, 096012 (2017); [arXiv:1702.06932 [nucl-th]]
  33. G. Chen, Yang Li, P. Maris, K. Tuchin and J.P. Vary, Diffractive charmonium spectrum in high energy collisions in the basis light-front quantization approach, Phys. Lett. B 769, 477 (2017); [arXiv:1610.04945 [nucl-th]]
  34. V.A. Karmanov, Yang Li, A.V. Smirnov and J.P. Vary, Nonperturbative solution of scalar Yukawa model in two- and three-body Fock space truncations, Phys. Rev. D 94, 096008 (2016); [arXiv:1610.03559 [hep-th]]
  35. Yang Li, P. Maris, X. Zhao and J.P. Vary, Heavy Quarkonium in a Holographic Basis, Phys. Lett. B 758, 118 (2016); [arXiv:1509.07212 [hep-ph]]; See Data.
  36. L. Adhikari, Yang Li, X. Zhao, P. Maris, J.P. Vary and A.A. El-Hady, Form Factors and Generalized Parton Distributions in Basis Light-Front Quantization, Phys. Rev. C 93, 055202 (2016); [arXiv:1602.06027 [nucl-th]]
  37. Yang Li, V.A. Karmanov, P. Maris and J.P. Vary, Ab Initio Approach to the Non-Perturbative Scalar Yukawa Model, Phys. Lett. B 748, 278 (2015); [arXiv:1504.05233 [nucl-th]]
  38. P. Wiecki, Yang Li, X. Zhao, P. Maris and J.P. Vary, Basis light-front quantization approach to positronium, Phys. Rev. D 91, 105009 (2015); [arXiv:1404.6234 [nucl-th]]
  39. S. Wu and Yang Li, Weak Measurement beyond the Aharonov-Albert-Vaidman formalism, Phys. Rev. A 83, 052106 (2011); [arXiv:1010.1155 [quant-ph]]

Reviews and Chapters

  1. James P. Vary, Yang Li, Chandan Mondal and Xingbo Zhao, Light-front quantization, in 50 Years of Quantum Chromodynamics, F. Gross and E. Klempt Eds., Eur. Phys. J. C 83, 1125 (2023)


Click titles to download slides.







  • Light-front spinors

    A Mathematica package that defines the gamma matrices and spinors used in light-front dynamics. See also my note, Spinors on the light front for details.

  • Talmi-Moshinsky in 2D

    Fortran and Mathematica codes to compute the 2D Talmi-Moshinsky transformation coefficients.

  • Color singlet

    A Mathematica package that computes the number of color singlets given the numbers of quarks, anti-quarks and gluons.
    Table of number of color singlets


  • Mendeley Data: Quarkonium light-front wave functions

    The set of data contains charmonium and bottomonium light-front wave functions obtained from the Basis Light-Front Quantization (BLFQ) approach with a running coupling as described in Yang Li, P. Maris, J.P. Vary, Quarkonium as relativistic bound state on the light front, Phys. Rev. D 96, 016022 (2017) ; [arXiv:1704.06968 [hep-ph]]. A visualization of the wave functions can be found in: Ancillary files for arXiv:1704.06968



  • 2010 - 2015: Iowa State University, Ph.D.
  • 2006 - 2010: University of Science and Technology of China, B.Sc.


  • 2021 - present: University of Science and Technology of China, Professor
  • 2020 - 2021: University of Chinese Academy of Sciences, Lecturer
  • 2018 - 2020: Iowa State University, Visiting Scientist
  • 2017 - 2018: College of William & Mary, Postdoctoral Research Associate
  • 2016 - 2017: Iowa State University, Postdoctoral Research Associate


  • Reviewer for Physical Review D, Journal of Physics G, Few-Body Systems


  • 2016, G.W. Fox Memorial Award, Department of Physics and Astronomy, Iowa State University
  • 2014, Gary McCartor Award, ILCAC

Invited Talks

See Talks