arXiv subjects

Shunrui Li

Publications and source records attributed to Shunrui Li.

5 recordsLinked to original sources

arXiv2026

Chern Character for Discrete Spectrum Partition Function

We establish a rigorous geometric correspondence between thermal partition functions of discrete-spectrum quantum systems with bounded ground energy and the Chern character of "virtual physical sheaf" over spacetime. By interpreting Hamiltonian dynamics as a $U(1)$-equivariant flow on the quantum phase space $\mathbb{CP}^n$ and pushforward to spacetime, we show that the finite-temperature partition function emerges as the integral of the Chern character of "virtual physical sheaf" over spacetime. The construction extends naturally to infinite dimensions through trace class guaranteed by Weyl's aspmtotic law. Using the Grothendieck-Riemann-Roch formalism, we prove pushforward invariance of the Chern character under thermal compactification on arbitrary manifolds, providing a topological foundation for thermal traces in quantum field theory. This framework unifies spectral theory with characteristic class theory, offering a geometric interpretation of partition functions based on operator-algebraic approach.

hep-th↗

arXiv2025

Non-SUSY physics and the Atiyah-Singer index theorem

The Atiyah-Singer index theorem, a cornerstone of modern mathematics, has traditionally been derived from supersymmetric (SUSY) physics. This paper demonstrates a direct derivation from non-supersymmetric quantum statistics by establishing a fundamental correspondence: the grand partition functions of non-interacting bosonic and fermionic systems are precisely the Chern characters of certain vector bundles. Furthermore, we generalize this correspondence to infinite dimensions, where we construct a novel mathematical framework of spectral-sheaf pairs. Within this framework, we formulate a generalized index theorem, identifying the topological index with a regularized spectral product. This work not only circumvents the need for supersymmetry but also provides a deeper unifying perspective, revealing quantum statistics as a sufficient foundation for topological invariants.

math-ph↗

arXiv2025

Quantum harmonic oscillator, index theorem and spectral asymmetry

We report a spectral asymmetry effect in the quantum harmonic oscillator, where its partition function is identified as the Chern character. This establishes a direct link between statistical mechanics, and topological invariants (Atiyah-Singer index theorem), revealing the internal energy as a non-SUSY manifestation of the index theorem. We show that the partition function can be interpreted as the Chern character of "virtual physical sheaf", namely, a Hermitian vector bundle encoding quantum states over spacetime. This work uncovers an underlying topological structure in bosonic quantum systems.

quant-ph↗

arXiv2024

Observational Tests of 4D Double Field Theory

Although General Relativity (GR) is a very successful theory of gravity, it cannot explain every observational phenomenon. People have tried many kinds of modified gravity theory to explain these phenomena which GR cannot explain very well, such as string theory. In recent years Double Field Theory (DFT) has been an exciting research area in string theory. The most general, spherically symmetric, asymptotically flat, static vacuum solution to D = 4 double field theory has been derived by S.M. Ko, J.H. Park and M. Suh. In this article, we calculate the minor corrections to the three predictions in GR: optical deflation, planet precession and gravitational redshift. These three predictions should be able to tested by observations and find the discrepancies between GR and DFT in the future.

hep-th↗

arXiv2024

Kerr-like metric in 4D Double Field Theory

Double Field Theory suggests that people can view the whole massless NS-NS sector as the gravitational unity. The $O(D,D)$ covariance and the doubled diffeomorphisms determine precisely how the Standard Model as well as a relativistic point particle should couple to the NS-NS sector. The theory also refines the notion of singularity. In [1], the authors derive analytically the most general, spherically symmetric, asymptotically flat, static vacuum solution to $D = 4$ Double Field Theory. The solution contains three free parameters and consequently generalizes the Schwarzschild geometry. In this paper, we generalize the metric in [1] to obtain the 'Kerr-like' metric in $D = 4$ double field theory (DFT) in the Einstein frame and string frame. Then we apply 'covariant phase space' approach to study the thermodynamic properties of the metric we have obtained. We explore the first law of black hole thermodynamics and Hawking radiation for this metric carefully. As a special case, the 'Schwarzschild-like' metric in $4D$ double field theory in [1] can be recovered.

hep-th↗