Related papers: Supernematic
Any quantum-mechanical system possesses a U(1) gerbe naturally defined on configuration space. Acting on Feynman's kernel exp(iS/h), this U(1) symmetry allows one to arbitrarily pick the origin for the classical action S, on a…
We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Locally constrained gauge theories underpin our understanding of fundamental interactions in particle physics and the emergent behaviour of quantum materials. In strongly correlated systems, they can give rise to quantum spin liquids that…
A version of the cosmological perturbation theory in general relativity (GR) is developed, where the cosmological scale factor is identified with spatial averaging of the metric determinant logarithm and the cosmic evolution acquires the…
We show that Hall conductance and its non-abelian and higher-dimensional analogs are obstructions to promoting a symmetry of a state to a gauge symmetry. To do this, we define a local Lie algebra over a Grothendieck site as a pre-cosheaf of…
Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body…
The quantum properties of localized finite energy solutions to classical Euler-Lagrange equations are investigated using the method of collective coordinates. The perturbation theory in terms of inverse powers of the coupling constant $g$…
A cosmology inspired structure for phase space is introduced, which leads to finitization and lattice-like discretization of position and momentum eigenvalues in a preferred, cosmic frame. Lorentz invariance is broken at very high energies,…
Magnetic instability in gapless superconductors still remains as a puzzle. In this article, we point out that the instability might be caused by using BCS theory in mean-field approximation, where the phase fluctuation has been neglected.…
A constraint correlation dynamics up to 4-point Green functions is proposed for SU(N) gauge theories which reduces the N-body quantum field problem to the two-body level. The resulting set of nonlinear coupled equations fulfills all…
A quantum model of neural network is introduced and its phase structure is examined. The model is an extension of the classical Z(2) gauged neural network of learning and recalling to a quantum model by replacing the Z(2) variables, $S_i =…
Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. A major challenge is to reproduce gauge invariance, as violations of this quintessential property of lattice gauge theories can have dramatic…
Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally…
We develop a mathematical framework for the quantum simulation of lattice gauge theories using gauge-invariant packaged quantum states \cite{Ma2017,Ma2025}. In this formalism, every single excitation transforms as a complete…
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…
Recent advances in cooling techniques make now possible the experimental study of quantum phase transitions, which are transitions near absolute zero temperature accessed by varying a control parameter. A paradigmatic example is the…
The modern description of elementary particles, as formulated in the Standard Model of particle physics, is built on gauge theories. Gauge theories implement fundamental laws of physics by local symmetry constraints. For example, in quantum…
A new class of models of dynamical supersymmetry breaking is proposed. The models are based on SU(N_C) gauge theories with N_F(<N_C) flavors of quarks and singlets. Dynamically generated superpotential exibits runaway behavior. By embedding…
$\mathcal{N}=1$ supersymmetric QCD (SQCD) is a possible building block of theories beyond the standard model. It describes the interaction between gluons and quarks with their superpartners, gluinos and squarks. Since supersymmetry is…