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Tong Chern

Publications and source records attributed to Tong Chern.

8 recordsLinked to original sources
arXiv2024

Solving Maxwell's Equations

This paper discusses the use of the Riemann-Silberstein vector to solve the source-free Maxwell's equations and obtains novel analytical solutions. The solving process naturally leads to the spinor form of the source-free Maxwell's equations. Several powerful theorems are established to solve this spinor form equation. The Waveguide Solution Theorem provides an elegant way to solve waveguide problems, while The Schrodinger Solution Theorem connects the Maxwell's equations with the two-dimensional Schrodinger equation. By utilizing The Schrodinger Solution Theorem, a precise formula for spatiotemporal diffraction of the Maxwell's equations is derived, which allows for the reconstruction of electromagnetic waves throughout space and time based on the field distribution on the diffraction screen. And finally, by studying some relevant contour integrals, two additional simple but beautiful mathematical theorems that are necessarily satisfied by electromagnetic field in any source-free region are derived.

physics.gen-ph↗
arXiv2016

Quantum Dualities and Quantum Anomalous Hall Phases with Arbitrary Large Chern Numbers

Quantum duality is a far reaching concept in contemporary theoretical physics. In the present paper, we reveal the quantum dualities in quantum anomalous Hall (QAH) phases through concrete two bands Hamiltonian models. Our models can realize QAH phases with arbitrary large Chern numbers. In real materials these models may be realized by stacked $n$ layer systems of $c_1=1$ QAH insulators. The topological phase transitions that can change the Chern numbers are studied. And we investigate the gapless edge modes of our models in details, and find a new mechanism for the bulk boundary correspondence.

cond-mat.mes-hall↗
arXiv2016

Simple Models for All Topological Phases

We construct simple models for all topological phases of free fermions. These explicit models can realize all the nontrivial topological phases (with any possible topological invariant) of the periodic table. Many well known models for topological insulators and superconductors are special cases of our general constructions.

cond-mat.mes-hall↗
arXiv2016

Models for $d$ Wave Topological Superconductors and Quantum Anomalous Hall Effect with Arbitrary Large Chern Numbers

We construct theoretical models for two dimensional(2d) chiral $d_{x^2-y^2}\pm id_{xy}$ topological superconductors and for three dimensional(3d) $d$ wave topological superconductors. Moreover we build models for any 2d class C and 3d class CI topological superconductors (with any even topological invariants). We also construct concrete models that can realize quantum anomalous Hall effect with arbitrary large Chern numbers. We study the chiral edge modes or gapless surface states of our 2d or 3d models in details. In all the cases, we find novel mechanisms that make the numbers of boundary states always agree with the nontrivial bulk topology, just as required by the bulk boundary correspondence.

cond-mat.mes-hall↗
arXiv2011

Vortex Operator and BKT Transition in Abelian Duality

We give a new simple derivation for the sine-Gordon description of Berezinskii-Kosterlitz-Thouless(BKT) phase transition (is driven by vortices). Our derivation is simpler than traditional derivations. Besides, our derivation is a continuous field theoretic derivation by using path integration, different from the traditional derivations which are based on lattice theory or based on Coulomb gas model. Our new derivation rely on Abelian duality of two dimensional quantum field theory. By utilizing this duality in path integration, we find that the vortex configurations are naturally mapped to exponential operators in dual description, these operators are the vortex operators that can create vortices, the sine-Gordon description then naturally follows. Our method may be useful for the investigation to the BKT physics of superconductors.

physics.gen-ph↗
arXiv2011

On Understanding and Machine Understanding

In the present paper, we try to propose a self-similar network theory for the basic understanding. By extending the natural languages to a kind of so called idealy sufficient language, we can proceed a few steps to the investigation of the language searching and the language understanding of AI. Image understanding, and the familiarity of the brain to the surrounding environment are also discussed. Group effects are discussed by addressing the essense of the power of influences, and constructing the influence network of a society. We also give a discussion of inspirations.

cs.AI↗
arXiv2010

Superconformal Field Theory In Six Dimensions And Supertwistor

We studied the quantum dynamics of six dimensional $\mathcal{N}=(2, 0)$ superconformal field theory (the QNG theory). We developed the spinor technique for six-dimensional quantum field theories. By combining this technique with the canonical quantization procedure, we can overcome the subtlety of the chiral nature of $\mathcal{N}=(2, 0)$ free tensor multiplet and work out its quantum mechanical theory. We then studied the $\mathbf{T}^2$ compactification of the QNG theory and argued that the resulting four dimensional quantum field theory is indeed the $\mathcal{N}=4$ super-Yang-Mills theory with the $SL(2, \mathbf{Z})$ duality coming from the mapping class symmetries of $\mathbf{T}^2$. We also investigated the BPS self-dual string excitations by proposing a CFT description to their world sheet theory. At last, we constructed the super-twistor space $\hat{\mathbb{PT}}$ that corresponded to the superconformal group $U^*Sp(4|2, \mathbf{H})\subset OSp(8|4, \mathbb{C})$, encoded the full free tensor multiplet into it and made some speculations on the possible super-twistor formulation of the QNG theory.

hep-th↗